Question

Factorise the expression and divide them as directed: $(m^2-14m-32)÷(m+2)$

Answer 1

Step 1: Factorize the given expression

Given expression is $m^2-14m-32$. Factorizing the expression by middle term split method, we get,

$$\begin{gathered} m^2-14m-32=m^2+2m-16m-32 \\ =m\left(m+2\right)-16\left(m+2\right) \\ \Rightarrow m^2-14m-32=\left(m+2\right)\left(m-16\right) \end{gathered}$$

Step 2: Solve for the required value

$$\begin{gathered} \frac{m^2-14m-32}{m+2}=\frac{\left(m+2\right)\left(m-16\right)}{m+2} \\ =m-16 \end{gathered}$$

Hence, the required answer is $m-16$