Phân tích thành nhân tử: ( bằng kĩ thuật tách hạng tử )
6x^2 - 13x + 6
6x^2 + 13x +6
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a. = \(6x^2+3x+12x+6=3x\left(2x+1\right)+6\left(2x+1\right)=\left(2x+1\right)\left(3x+6\right)=3\left(2x+1\right)\left(x+2\right)\)
b. \(=6x^2-3x-12x+6=3x\left(2x-1\right)-6\left(2x-1\right)=3\left(2x-1\right)\left(x-2\right)\)
c. \(=6x^2+2x+18x+6=2x\left(3x+1\right)+6\left(3x+1\right)=\left(2x+6\right)\left(3x+1\right)=2\left(x+3\right)\left(3x+1\right)\)
d. \(=6x^2-2x-18x+6=2x\left(3x-1\right)-6\left(3x-1\right)=2\left(x-3\right)\left(3x-1\right)\)
(+) 6x^2 + 15x + 6 = 6x^2 + 12x + 3x + 6
= 6x ( x+ 2 ) + 3 ( x + 2)
= ( 6x + 3) ( x + 2 )
= 3 (2 x + 1 ) ( x + 2)
(+) 6x^2 - 15x + 6 = 6x^2 - 3x - 12x + 6
= 3x( 2x - 1 ) - 6 ( 2x - 1 )
= ( 3 x - 6 )( 2x - 1)
= 3 ( x- 2 ) (2x- 1)
1) 6x^2 + 7x - 5
=6x2-3x+10x-5
=3x.(2x-1)+5.(2x-1)
=(2x-1)(3x+5)
2) 10x^2 - 13x - 3
=10x2+2x-15x-3
=2x(5x+1)-3(5x+1)
=(5x+1)(2x-3)
\(6x^2+7x-5\)
\(=6x^2-3x+10x-5\)
\(=3x\left(2x-1\right)+5\left(2x-1\right)\)
\(=\left(2x-1\right)\left(3x+5\right)\)
Bài làm:
Ta có: \(3x^2+3x-6\)
\(=\left(3x^2+6x\right)-\left(3x+6\right)\)
\(=3x\left(x+2\right)-3\left(x+2\right)\)
\(=3\left(x-1\right)\left(x+2\right)\)
\(3x^2+3x-6\)
\(=3\left(x^2+x-2\right)\)
\(=3\left(x^2+2x-x-2\right)\)
\(=3\left[x\left(x+2\right)-\left(x+2\right)\right]\)
\(=3\left(x-1\right)\left(x+2\right)\)
=6x^2 - 4x - 9x +6
=(6x^2 -4x) - (9x-6)
=2x(3x -2) - 3(3x-2)
=(3x-2) (2x - 3)
\(1,2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(2x+1\right)\left(x-2\right)\)
\(2,4x^2-7x-2\)
\(=4x^2-8x+x-2\)
\(=4x\left(x-2\right)+x-2\)
\(\left(4x+1\right)\left(x-2\right)\)
Ta có: \(-8x^2+23x+3\)
\(=\left(-8x^2+24x\right)-\left(x-3\right)\)
\(=-8x\left(x-3\right)-\left(x-3\right)\)
\(=\left(-8x-1\right)\left(x-3\right)\)
\(=\left(3-x\right)\left(8x+1\right)\)
\(-8x^2+23x+3\)
\(=-\left(8x^2-23x-3\right)\)
\(=-\left(8x^2-24x+x-3\right)\)
\(=-\left[8x\left(x-3\right)+\left(x-3\right)\right]\)
\(=-\left(8x+1\right)\left(x-3\right)\)
a. \(=6x^2-4x-9x+6=2x\left(3x-2\right)-3\left(3x-2\right)=\left(3x-2\right)\left(2x-3\right)\)
b. \(=6x^2+4x+9x+6=2x\left(3x+2\right)+3\left(3x+2\right)=\left(3x+2\right)\left(2x+3\right)\)
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