Question

On dividing $p\left(4p^2-16\right)$ by $4p\left(p-2\right)$, we get -

• A. $\text{2p+4}$
• B. $\text{2p-4}$
• C. $\text{p+2}$
• D. $\text{p-2}$

Answer 1

The correct option is C

$\text{p+2}$

Dividing the given polynomials using factorization method:

$$\begin{gathered} \text{p}\left(4p^2-16\right)÷4p\left(p-2\right)=\frac{\text{p}\left(4p^2-16\right)}{\text{4p}\left(p-2\right)} \\ =\frac{\text{4p}\left(p^2-4\right)}{\text{4p}\left(p-2\right)}\left(\text{taking 4 as common from the numerator}\right) \\ =\frac{\left({\text{p}}^2{\text{-2}}^2\right)}{\text{p-2}}\left({\text{cancelling common terms and rewritting 4 as 2}}^2\right) \\ =\frac{\left(\text{p+2}\right)\left(\text{p-2}\right)}{\text{p-2}}\left(\text{using the identity}\left(a^2-b^2\right)\text{=}\left(a+b\right)\left(a-b\right)\right) \\ =p+2\text{(cancelling common terms)} \end{gathered}$$

Hence, the correct option is C.