Question

Factorise : $x^3+6x^2+11x+6$

Answer 1

Given expression,$f\left(x\right)=x^3+6x^2+11x+6$

Put, $x=-1$

$f(-1)=-1^3+6{(-1)}^2+11(-1)+6=0$

Again put $x=-2$

$f(-2)={(-2)}^3+6{(-2)}^2+11(-2)+6=0$

Again put x= -3 we get,

$f(-3)={(-3)}^3+6{(-3)}^2+11(-3)+6=0$

Hence,

$x^3+6x^2+11x+6=(x-1)(x-2)(x-1)$

Hence, this is the answer.