Question

Workout the following divisions
$36(x+4)(x^2+7x+10)÷9(x+4)$

• A. $(x^2+7x+10)$
• B. $4(x^2+7x+6)$
• C. $4(x^2+7x+10)$
• D. None

Answer 1

The correct option is C $4(x^2+7x+10)$

We divide the given polynomial $36(x+4)(x^2+7x+10)$ by $9(x+4)$ as shown below:

$\frac{36(x+4)(x^2+7x+10)}{9(x+4)}=\frac{36}{9}\times \frac{(x+4)(x^2+7x+10)}{(x+4)}=\frac{2\times 2\times 3\times 3}{3\times 3}\times (x^2+7x+10)=4(x^2+7x+10)$

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