Question

Facsorise


${x}^{3} + {6}^{2} + 11x + 6$
​

Answer 1

We're actually given the cubic polynomial,

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

So,

$\begin{aligned}&x^3+6x^2+11x+6\\\\\implies\ \ &x^3+x^2+5x^2+5x+6x+6\\\\\implies\ \ &x^2(x+1)+5x(x+1)+6(x+1)\\\\\implies\ \ &(x+1)(x^2+5x+6)\\\\\implies\ \ &(x+1)(x^2+2x+3x+6)\\\\\implies\ \ &(x+1)(x(x+2)+3(x+2))\\\\\implies\ \ &(x+1)(x+2)(x+3)\end{aligned}$

Hence Factorized!