Question

Divide$\left\{52\right(m^4-5m^3-24m^2\left)\right\}\text{by}\left\{13m\right(m-8\left)\right\}.$

• A. $4m(m-3)$
• B. $4m(m+3)$
• C. $4m(m-4)$
• D. $4m(m+4)$

Answer 1

The correct option is B $4m(m+3)$

Given:
$\frac{52(m^4-5m^3-24m^2)}{13m(m-8)}$
Consider the numerator, $52(m^4-5m^3-24m^2)=2\times 2\times 13\times (m^4-5m^3-24m^2)$
$=2\times 2\times 13\times m^2(m^2-5m-24)...\left(i\right)$

Comparing the expression
$m^2-5m-24$ with the identity $x^2+(a+b)x+ab,(a+b)=-5andab=-24.$
$So,(-8)+3=-5\text{and}(-8)\left(3\right)=-24$
Hence, $m^2-5m-24=m^2-8m+3m-24$
$=m(m-8)+3(m-8)$
$=(m+3)(m-8)$
Substituting this in $\left(i\right)$
$=2\times 2\times 13\times m^2(m-8)(m+3)$

Therefore,
$\frac{52(m^4-5m^3-24m^2)}{13m(m-8)}=\frac{2\times 2\times 13\times m\times m\times (m-8)\times (m+3)}{13\times m\times (m-8)}$
$=2\times 2\times m\times (m+3)$
$=4m(m+3)$