Question

$\text{Divide}(a^2+7a+10)\text{by}(a+5).$

• A. 1
• B. $(a+1)$
• C. 2
• D. $(a+2)$

Answer 1

The correct option is D $(a+2)$

$\text{Given:}\frac{a^2+7a+10}{(a+5)}...\left(i\right)$

Comparing $a^2+7a+10$ with the identity $x^2+(a+b)x+ab,$
$\text{we note that,}(a+b)=7andab=10$
$So,5+2=7and\left(5\right)\left(2\right)=10$

Hence,
$a^2+7a+10$
$=a^2+5a+2a+10$
$=a(a+5)+2(a+5)$
$=(a+2)(a+5)$

From (i), we get
$\frac{a^2+7a+10}{(a+5)}=\frac{(a+2)(a+5)}{(a+5)}$
$=(a+2)$