Question

$36(x+4)(x^2+7x+10)÷9(x+4)$

Answer 1

We need to divide the polynomial $36(x+4)(x^2+7x+10)$ by the binomial $9(x+4)$.

Hence, $\frac{36(x+4)(x^2+7x+10)}{9(x+4)}$

$=\frac{9(x+4)}{9(x+4)}\times 4(x^2+7x+10)$

$=4(x^2+7x+10)$

$=4(x^2+5x+2x+10)$

$=4\left[x\right(x+5)+2(x+5\left)\right]$

$=4\left[\right(x+2\left)\right(x+5\left)\right]$

$=4(x+2)(x+5)$

Hence, $36(x+4)(x^2+7x+10)÷9(x+4)=4(x+2)(x+5)$.