Question

Factorize:

$\left(1\right)x^3-{2x}^2-x+2\left(2\right)x^3-{3x}^2-9x-5\left(3\right)x^3+{13x}^2+32x+20\left(4\right)y^3+y^2-y-1$

Answer 1

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

$=x^2(x-2)-1(x-2)$

$=(x-2)(x^2-1)$

$=(x-2)(x-1)(x+1)$

(2) $x^3-3x^2-9x-5$

$=x^3+(x^2-4x^2)-(4x+5x)-5$

$=(x^3+x^2)-(4x^2+4x)-(5x+5)$

$=x^2(x+1)-4x(x+1)-5(x+1)$

$=(x^2-4x-5)(x+1)-5(x+1)$

$=(x^2-4x-5)(x+1)$

$=(x^2-5x+x-5)(x+1)$

$=(x-5)(x+1{)}^2$

(3) $x^3+13x^2+32x+20$

$=(x^3+x^2)+(12x^2+12x)+(20x+20)$

$=(x^2+12x+20)(x+1)$

$(x+1)(x+2)(x+10)$

(4) $y^3+y^2-y-1=y^2(y+1)-1(y+1)$

$=(y^2-1)(y+1)$

$=(y-1)(y+1{)}^2$