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a) -8x2+5x+3=-8x^2+8x-3x+3=-8x(x-1)-3(x-1)=-(8x+3)(x-1)
b)8x^2-10x-3=8x^2-12x+2x-3=8x(x-1,5)+2(x-1,5)=2(4x+1)(x-1,5)
c)=8x^2-2x+12x-3=2x(4x-1)+3(4x-1)=(2x+3)(4x-1)
d)=-8x^2+24x-x+3=-8x(x-3)-(x-3)=-(8x+1)(x-3)
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. \(=6x^2+4x+9x+6=2x\left(3x+2\right)+3\left(3x+2\right)=\left(3x+2\right)\left(2x+3\right)\)
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)
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) x2 - 7x + 5 = ( x2 - 2 . 7/2 . x + 49 / 4 ) + 5 - 49 / 4
= (x - 7/2)^2 - 29/4
= (x - 7/2)^2 - (√ 29 / 2 )^2
= ( x - ( 7 + √ 29 / 2 )). ( x + ( 7 - √ 29 / 2 ))
\(2x-1^3+8\)
\(=2x-9\)
\(=\left(\sqrt{2x}\right)^2-3^2\)
\(=\left(\sqrt{2x}-3\right)\left(\sqrt{2x}+3\right)\)
_________
\(8x^3-12x^2+6x-1\)
\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\)
\(=\left(2x-1\right)^3\)
_______________
\(8x^3-12x^2+6x-2\)
\(=8x^3-12x^2+6x-1-1\)
\(=\left(2x-1\right)^3-1\)
\(=\left(2x-1-1\right)\left(4x^2-4x+1+2x-1+1\right)\)
\(=\left(2x-2\right)\left(4x^2-2x+1\right)\)
\(=2\left(x-1\right)\left(4x^2-2x+1\right)\)
________
\(9x^3-12x^2+6x-1\)
\(=x^3+8x^3-12x^2+6x-1\)
\(=x^3+\left(2x-1\right)^3\)
\(=\left(x+2x-1\right)\left(x^2-2x^2-x+4x^2-4x+1\right)\)
\(=\left(3x-1\right)\left(3x^2-5x+1\right)\)
b: 8x^3-12x^2+6x-1
=(2x)^3-3*(2x)^2*1+3*2x*1^2-1^3
=(2x-1)^3
c: =(8x^3-12x^2+6x-1)-1
=(2x-1)^3-1
=(2x-1-1)[(2x-1)^2+2x-1+1]
=2(x-1)(4x^2-4x+1+2x)
=2(x-1)(4x^2-2x+1)
a)3x2+7x-6
=3x2-2x+9x-6
=x(3x-2)+3(3x-2)
=(x+3)(3x-2)
b)8x2-2x-3
=8x2-6x+4x-3
=2x(4x-3)+(4x-3)
=(2x+1)(4x-3)
c)6x2-15x+6
=3(2x2-5x+2)
=3(2x2-x-4x+2)
=3[x(2x-1)-2(2x-1)]
=3(x-2)(2x-1)
d)10x2+7x-6
=10x2+12x-5x-6
=2x(5x+6)-(5x+6)
=(2x-1)(5x+6)
\(1,2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(2x+1\right)\left(x-2\right)\)
\(2,4x^2-7x-2\)
\(=4x^2-8x+x-2\)
\(=4x\left(x-2\right)+x-2\)
\(\left(4x+1\right)\left(x-2\right)\)
a. \(=6.\left(x^2+2x+1\right)=6\left(x+1\right)^2\)
b. \(=8x^2-6x+4x-3=2x\left(4x-3\right)+\left(4x-3\right)=\left(2x+1\right)\left(4x-3\right)\)
c. \(=8x^2+6x-4x-3=2x\left(4x+3\right)-\left(4x+3\right)=\left(2x-1\right)\left(4x+3\right)\)