Question

Factorise: $x^3+13x^2+32x+20$.

Answer 1

Solution:-

Let $p\left(x\right)=x^3+13x^2+32x+20$

$P(-1)={(-1)}^3+13{(-1)}^2+32(-1)+20=0$

$\therefore (x+1)$ is a factor of $p\left(x\right)$.

On dividing $p\left(x\right)$ by $(x+1)$, we get

$p\left(x\right)÷(x+1)=x^2+12x+20$

$\therefore x^3+13x^2+32x+20=(x+1)(x^2+12x+20)$

$\Rightarrow =(x+1)(x^2+10x+2x+20)$

$\Rightarrow =(x+1)[x(x+10)+2(x+10)]$

$\Rightarrow =(x+1)\left[(x+10)(x+2)\right]$

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

Hence, $x^3+13x^2+32x+20=(x+1)(x+2)(x+10)$