Question

3(x+2)^2 - 5(x+2)+2 factorize

Answer 1

let x+2=y
3y^2-5y+2=0
3y^2-2y-3y+2=0
y(3y-2)-(3y-2)=0
(3y-2)(y-1)=0
y=3/2    y=1
x+2=3/2     x+2=1
x=-1/2        x=-1

Answer 2

$3( {x}^{2} + 4 + 4x) - 5x - 10 + 2 \\ 3 {x}^{2} + 12 + 12x - 5x - 10 + 2 \\ 3 {x}^{2} + 7x + 4 \\ 3 {x}^{2} + (4 + 3)x + 4 \\ 3 {x}^{2} + 4x + 3x + 4 \\ x(3x + 4) + 1(3x + 4) \\ (x + 1) (3x + 4) \\ x = - 1 \\ x = - \frac{4}{3}$