Question

$\text{Divide}(m^2+7m-60)\text{by}(m+12).$

• A. 4(m-6)
• B. 2(m+6)
• C. (m-5)
• D. (m-12)

Answer 1

The correct option is C (m-5)

$\text{Given,}\frac{m^2+7m-60}{(m+12)}...\left(i\right)$

Comparing $m^2+7m-60$ with the identity $x^2+(a+b)x+ab,$
$\text{we note that,}(a+b)=7\text{and}ab=-60$

$So,12+(-5)=7\text{and}\left(12\right)(-5)=-60$

Hence,
$m^2+7m-60$
$=m^2+12m-5m-60$
$=m(m+12)-5(m+12)$
$=(m-5)(m+12)$

From (i), we get,
$\frac{m^2+7m-60}{(m+12)}=\frac{(m-5)(m+12)}{(m+12)}=(m-5)$