Question

Factorize the expression and divide them as directed: $(x^3+x^2-132x)÷x(x-11)$

Answer 1

Step 1: Factorise the expression
$x^3+x^2-132x$
$=x(x^2+x-132)$
$=x[x^2+(12-11)x-132]$
$=x[x^2+12x-11x-132]$
$=x\left[x\right(x+12)-11(x+12\left)\right]$
$=x\left[\right(x-11\left)\right(x+12\left)\right]$

Step 2: Perform the division of the given expression
$\frac{x^3+x^2-132x}{x(x-11)}=\frac{x(x-11)(x+12)}{x(x-11)}$
$=(x+12)$
$\therefore (x^3+x^2-132x)÷x(x-11)=(x+12)$