Question

Find the integral roots of the polynomial $f\left(x\right)=x^3+6x^2+11x+6$ ?

Answer 1

Let p(x) $=x^3+{6x}^2+11x+6$

Put $x=–1$

$p(–1)$ $=(–1{)}^3+{6(–1)}^2+11(–1)+6=–1+6–11+6=0$

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

So, we cam break up terms of $p\left(x\right)$ as follows.

$p\left(x\right)=x^3+{6x}^2+11x+6$

Therefore, the integral roots of the given equation is find out as:

$p\left(x\right)=0$

$(x+1)(x+2)(x+3)=0$

$x=-1,-2,-3$