Question

1)    x³ + 2x² - 2x - 1

2)    4x(x - 3y )+ 12y(3y - x)

Answer 1

\(x^3+2x^2-2x-1\)

\(=\left(x-1\right)\left(x^2+x+1\right)+2x\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+3x+1\right)\)

Answer 2

1. x³ + 2x² - 2x - 1

= (x³ - 1) + (2x² - 2x) 

= (x - 1)(x² + 2x + 1) + 2x(x - 1)

= (x² + 2x + 1 + 2x)(x - 1)

= (x² + 4x + 1)(x - 1)

2. 4x(x - 3y) + 12y(3y - x)

= 4x(x - 3y) - 12y(x - 3y)

= (4x - 12y)(x - 3y)

= 4(x - 3y)(x - 3y)

= 4(x - 3y)²

Answer 3

1) x³+2x²-2x-1

=  (x³-1)+(2x²-2x)

= 2x(x-1)(x²+x+1)(x-1)

=2x(x²+x+1)(x-1)²

Answer 4

2) 4x(x-3y)+12(3y-x)

= 4x(x-3y)-12(x-3y)

=(x-3y)(4x-12)

= 4(x-3y)(x-3)