Simplify (4x^4+8x^3)/(x^2-2x-8)

Factor ${\displaystyle 4x^3}$ out of ${\displaystyle 4x^4}$.

Factor ${\displaystyle 4x^3}$ out of ${\displaystyle 8x^3}$.

Factor ${\displaystyle 4x^3}$ out of ${\displaystyle 4x^3\left(x\right)+4x^3\left(2\right)}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -8}$ and whose sum is ${\displaystyle -2}$.

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.