Question

Factories:
$x^3+13x^2+32x+20$

Answer 1

$x^3-13x^2+32x+20$

$=x^3+13x^2+30x+2x+20$

$=x(x^2+13x+30)+2x+20\left[\text{Taking x as common}\right]$

$=x(x^2+\underset{–}{10x+3x}+30)+2(x+10)$

$=x\left\{x\right(x+10)+3(x+10\left)\right\}+2(x+10)$

$=x(x+3)(x+10)+2(x+10)$

$=(x+10)\left\{x\right(x+3)+2\}$

$=(x+10)(x^2+3x+2)$

$=(x+10)(x^2+2x+x+2)$

$=(x+10)\left\{x\right(x+2)+1(x+2\left)\right\}$

$=(x+10)\left\{\right(x+1\left)\right(x+2\left)\right\}$

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