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a: \(=\left(x+1\right)\left(x^2-x+1\right)+5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+4x+1\right)\)
a: \(-6x^2+7x-2\)
\(=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(-3x+2\right)\)
b: \(2x^2-5x+2\)
\(=2x^2-4x-x+2\)
\(=2x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-1\right)\)
a: =2(x-2)+y(x-2)
=(x-2)(2+y)
b: \(=\left(x+y\right)^2-4=\left(x+y+2\right)\left(x+y-2\right)\)
c: =(x-7)(x+2)
a.
2x - 4 + xy - 2y
= 2(x-2) +y(x-2)
= (x-2)(y+2)
c.
x^2 - 5x - 14
= x^2 + 2x - 7x - 14
= x(x+2) - 7(x+2)
= (x-7)(x+2)
\(2x^2-7x+5=\left(2x^2-2x\right)-\left(5x-5\right)=2x\left(x-1\right)-5\left(x-1\right)=\left(2x-5\right)\left(x-1\right)\)
\(3x^2+5x+2=\left(3x^2+3x\right)+\left(2x+2\right)=3x\left(x+1\right)+2\left(x+1\right)=\left(3x+2\right)\left(x+1\right)\)
a: \(2x^2-7x+5=\left(x-1\right)\left(2x-5\right)\)
b: \(3x^2+5x+2=\left(x+1\right)\left(3x+2\right)\)
a) \(4\left(x+1\right)^3-x-1=4\left(x+1\right)^3-\left(x+1\right)=\left(x+1\right)\left[4\left(x+1\right)^2-1\right]=\left(x+1\right)\left[2\left(x+1\right)-1\right]\left[2\left(x+1\right)+1\right]=\left(x+1\right)\left(2x+1\right)\left(2x+3\right)\)
b) \(5x\left(x-3\right)+\left(3-x\right)^2-\left(x-3\right)=5x\left(x-3\right)+\left(x-3\right)^2-\left(x-3\right)=\left(x-3\right)\left(5x+x-3-1\right)=\left(x-3\right)\left(6x-4\right)=2\left(x-3\right)\left(3x-2\right)\)
c) \(9x^2y^3-3x^4y^2-6x^3y^2+16xy^4=xy^2\left(9xy-3x^3-6x^2+16y^2\right)\)
a. 5x3-10x2+5x
= 5x(x2-2x+1)
= 5x(x-1)2