PHAN TICH DA THUC THANH NHAN TU
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<span class='text_page_counter'>(1)</span>PHÂN TÍCH ĐA THỨC THÀNH NHÂN TỬ Phương pháp đặt nhân tử chung 1. Phân tích thành nhân tử: a) 3x 6y = ............................................................ 2 2 x 5x 3 x 2 y b) 5 =................................................ 2 2 2 2 c) 14x y 21xy 28x y = ..................................... ............................................................................. 2 2 x(y 1) y(y 1) 5 d) 5 =......................................... n 1 n 4. Chứng minh rằng 55 55 chia hết cho 54 n 1 n Ta có: 55 55 = .................................................. .................................................................................. Vì ............................................................................. n 1 n Vậy: 55 55 chia hết cho 54.. Phương pháp dùng hằng đẳng thức 5. Phân tích thành nhân tử:. e) 10x(x y) 8y(y x) =........................................ 2 a) x 4x 4 = ........................................................ .............................................................................. 2 b) x 2 =.................................................................. 2. Tính giá trị của biểu thức:. 3 c) 1 8x = ................................................................ a) 15.91,5 150.0,85 = ............................................ 3 2 d) x 3x 3x 1 = ................................................. .............................................................................. 2 2 e) (x y) 9x = ..................................................... ............................................................................. b) x(x 1) y(1 x) tại x = 2001 và y = 1999 Ta có x(x 1) y(1 x) = ................................... .............................................................................. ............................................................................. 2 f) x 6x 9 = ........................................................ 2 g) 10x 25 x = ...................................................... .............................................................................. ............................................................................. ............................................................................. ............................................................................. 3. Tìm x, biết: a) 5x(x 2000) x 2000 0 ......................................................................... ......................................................................... ......................................................................... ......................................................................... Vậy ...................................................................... 3 b) x 13x 0 ......................................................................... ......................................................................... ......................................................................... ......................................................................... .......................................................................... Vậy........................................................................ h). 8x 3 . 1 8 = ............................................................... 1 2 x 64y 2 25 i) = ..................................................... ............................................................................. j). x3 . 1 27 = .............................................................. ............................................................................. 3 3 k) (a b) (a b). = .......................................................................... =........................................................................... =........................................................................... =........................................................................... =........................................................................... 3 3 l) (a b) (a b). = ...........................................................................
<span class='text_page_counter'>(2)</span> =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ 3 2 m) x 9x 27x 27 = ......................................... .............................................................................. =........................................................................... =............................................................................ 6. Tìm x, biết: 2 a) 2 25x 0 ......................................................................... ......................................................................... ......................................................................... .......................................................................... Vậy ...................................................................... 1 x x 0 4 b) ......................................................................... ......................................................................... ......................................................................... ......................................................................... 2. Vậy ...................................................................... 7. Tính nhanh:. =........................................................................... b) 2xy 3z 6y xz Cách 1. Ta có 2xy 3z 6y xz =........................................................................... =........................................................................... =........................................................................... =........................................................................... Cách 2. Ta có 2xy 3z 6y xz =........................................................................... =........................................................................... =........................................................................... =........................................................................... 4 3 2 c) x 9x x 9x. 2 2 a) 73 27 = .......................................................... 2 2 b) 37 13 = .......................................................... 2. 2 Cách 2. Ta có x 3x xy 3y. 2. c) 2002 2 = ........................................................ 2 8. Chứng minh rằng ( 2n 5) 25 chia hết cho 4,. với n là số nguyên dương.. 4 3 2 Cách 1. Ta có x 9x x 9x. =........................................................................... =........................................................................... =........................................................................... =........................................................................... 4 3 2 Cách 2. Ta có x 9x x 9x. 2 Ta có: (2n 5) 25 = ............................................. =............................................................................ ................................................................................... =............................................................................ ................................................................................... =............................................................................ Vì .............................................................................. =............................................................................ 2 Vậy: (2n 5) 25 chia hết cho 4.. Phương pháp nhóm hạng tử 9. Phân tích thành nhân tử: 2 a) x 3x xy 3y 2. Cách 1. Ta có x 3x xy 3y. 2 d) x xy x y 2 Cách 1. Ta có x xy x y. =........................................................................... =........................................................................... =........................................................................... =............................................................................
<span class='text_page_counter'>(3)</span> 2 Cách 2. Ta có x xy x y. 2 2 2 2 Ta có x 2xy y z 2zt t. =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ e) xz yz 5(x y). =............................................................................ Cách 1. Ta có xz yz 5(x y) =........................................................................... =............................................................................ =........................................................................... 10. Tính nhanh: a) 15.64 25.100 36.15 60.100. =............................................................................ = ........................................................................... Cách 2. Ta có xz yz 5(x y). =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =........................................................................... =............................................................................ b) 37,5.6,5 7,5.3, 4 6, 6.7,5 3,5.37,5 = .......................................................................... =............................................................................ 2 f) 3x 3xy 5x 5y 2 Cách 1. Ta có 3x 3xy 5x 5y. =........................................................................... =........................................................................... =........................................................................... 2 Cách 2. Ta có 3x 3xy 5x 5y. =........................................................................... =........................................................................... =........................................................................... 2 2 2 c) 45 40 15 80.45. = .......................................................................... =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =........................................................................... 2. 2. g) x 4x y 4 2. Phương pháp dùng tách và thêm bớt hạng tử. 2. Ta có x 4x y 4 =........................................................................... =........................................................................... =........................................................................... 2. 2. h) 3x 6xy 3y 3z 2. 2. 11. Phân tích thành nhân tử: 2 a) x 3x 2. += =. Cách 1. (Tách 3x ...............................................) 2 Ta có x 3x 2 =............................................... =........................................................................... 2. Ta có 3x 6xy 3y 3z. 2. =............................................................................ =............................................................................ Cách 2. (Tách 2 = ...................................................). =............................................................................ 2 Ta có x 3x 2 =............................................... =........................................................................... 2 2 2 2 i) x 2xy y z 2zt t. =........................................................................... =............................................................................
<span class='text_page_counter'>(4)</span> Cách 3. (Tách 2 = ...................................................) 2 Ta có x 3x 2 =............................................... =........................................................................... =........................................................................... 2. Cách 4. (Tách x = ..................................................) 2. Ta có x 3x 2 =.............................................. =........................................................................... =........................................................................... =........................................................................... 2 b) x x 6. += =. Cách 1. (Tách x = ...................................................) 2 Ta có x x 6 =................................................. =........................................................................... =........................................................................... Cách 2. (Tách – 6 = ...............................................) 2 Ta có x x 6 =................................................. =........................................................................... =........................................................................... Cách 3. (Tách – 6 = ...............................................) 2 Ta có x x 6 =................................................. =........................................................................... =........................................................................... 2 c) x 5x 6. += Cách 1. (Tách 5x = .................................................) = 2 Ta có x 5x 6 =............................................... =........................................................................... =........................................................................... Cách 2. (Tách 6 = .................................................) 2 Ta có x 5x 6 =............................................... =........................................................................... =........................................................................... Cách 3. (Tách 6 = .................................................) 2 Ta có x x 6 =................................................. =........................................................................... =............................................................................ 2 d) x 4x 3. += Cách 1. (Tách – 4x = .............................................) = 2 Ta có x 4x 3 =............................................... =........................................................................... =........................................................................... 2 e) x 5x 4. +=. Cách 1. (Tách 5x = ................................................) = 2 Ta có x 5x 4 =............................................... =........................................................................... =........................................................................... 2 f) x x 6. +=. Cách 1. (Tách – x = ...............................................) = 2 Ta có x x 6 =................................................. =........................................................................... =........................................................................... 4 g) x 4 2 Cách 1. (Thêm bớt 4x ) 4 4 2 2 Ta có x 4 = x 4x 4 4x. = .......................................................................... =........................................................................... =............................................................................ Phương pháp tổng hợp 12. Phân tích thành nhân tử: 3 2 2 a) 5x 10x y 5xy =.......................................................................... =........................................................................... 2 2 b) x 2xy y 9. =.......................................................................... =........................................................................... 3 3 2 c) 2x y 2xy 4xy 2xy. =.......................................................................... =........................................................................... =........................................................................... =........................................................................... =............................................................................
<span class='text_page_counter'>(5)</span> =............................................................................ 2 2 d) x 4x 2xy 4y y. =........................................................................... 2 2 k) x 3x 4x 12. =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =........................................................................... =............................................................................ 3 2 2 e) x 2x y xy 9x. =.......................................................................... =............................................................................ =........................................................................... 4 2 l) x 5x 4. =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ 2 2 f) 2x 2y x 2xy y. =............................................................................ =........................................................................... 4 2 m) x 4x 3. =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ 4 2 g) x 2x. 4 2 n) x x 6. =............................................................................ =............................................................................ =............................................................................ =........................................................................... =............................................................................ 2 2 h) x 4 (x 2). =........................................................................... =............................................................................ =........................................................................... 4 2 o) x 5x 6. =............................................................................ =............................................................................ =............................................................................ =............................................................................ =............................................................................ 3 2 2 i) x 2x x xy. =........................................................................... =............................................................................ =........................................................................... 13. Tìm x, biết:. =........................................................................... =........................................................................... =........................................................................... 3 2 j) x 4x 12x 27. =........................................................................... =........................................................................... =........................................................................... =............................................................................ a). x2 . 1 x 0 4. ............................................................................. ............................................................................. ............................................................................. ............................................................................. 2 2 b) (2x 1) (x 3) 0. ..............................................................................
<span class='text_page_counter'>(6)</span> ............................................................................. ............................................................................. .............................................................................. 1 1 A x 2 x 2 16 tại x = 49,75 a). .............................................................................. 1 1 A x 2 x 2 16 = ................................. Ta có:. .............................................................................. .............................................................................. .............................................................................. Thay ..................................................................... 2. c) x (x 3) 12 4x 0 ............................................................................. ............................................................................. .............................................................................. ............................................................................. 2 2 b) B x y 2y 1 tại x = 93 và y = 6 2 2 Ta có B x y 2y 1 = ................................ .............................................................................. =............................................................................ .............................................................................. =............................................................................ .............................................................................. =............................................................................ 2 x(x 2 4) 0 3 d) ............................................................................. ............................................................................. .............................................................................. Thay..................................................................... B =........................................................................ 2 2 c) C x 4y 4xy tại x = 18 và y = 4 2 2 Ta có C x 4y 4xy = ................................ .............................................................................. =............................................................................ .............................................................................. Thay...................................................................... .............................................................................. C = ........................................................................ 2 e) (x 2) (x 2)(x 2) 0. ............................................................................. ............................................................................. ............................................................................. ............................................................................. ............................................................................. ............................................................................. ............................................................................. 2 3 f) x 2 2x 2x 0. 3 2 2 3 d) D 8x 12x y 6xy y tại x = 6 và y = – 8 3 2 2 3 Ta có D 8x 12x y 6xy y. =........................................................................... =........................................................................... Thay..................................................................... D = ...................................................................... 2 2 e) E 1, 6 4 . 0, 8 . 3, 4 3, 4 2 2 Ta có E 1, 6 4 . 0,8 . 3, 4 3, 4. .............................................................................. =............................................................................ .............................................................................. =............................................................................ .............................................................................. = ........................................................................... ............................................................................. ............................................................................. ............................................................................. 14. Tính nhanh giá trị biểu thức sau:. 4 4 2 2 f) F 3 .5 (15 1)(15 1) 4 4 2 2 Ta có F 3 .5 (15 1)(15 1). =........................................................................... =........................................................................... = ...........................................................................
<span class='text_page_counter'>(7)</span> 4 3 2 g) G x 12x 12x 111 tại x = 11 4 3 2 Ta có G x 12x 12x 111. =........................................................................... =........................................................................... Thay..................................................................... G = ...................................................................... 3 15. Chứng minh rằng n n chia hết cho 6, với n. là số nguyên. 3 Ta có: n n = ......................................................... .................................................................................. .................................................................................. Vì ............................................................................. Vậy: .......................................................................... = dcvsdvvvvvfdf.
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