Question

$(3p^3-9p^{2}q-6p{q}^2)÷(-3p)$

• A. $(2q^2+3pq+p^2)$
• B. $(2q^2+pq-p^2)$
• C. $(2q^2+3pq-p^2)$
• D. None

Answer 1

Answer: (C)

$(2q^2+3pq-p^2)$

We divide the given polynomial $3p^3-9p^{2}q-6p{q}^2$ by the monomial $-3p$ as shown below:

$\Rightarrow \frac{3p^3-9p^{2}q-6p{q}^2}{-3p}=\frac{3p^3}{-3p}-\frac{9p^{2}q}{-3p}-\frac{6p{q}^2}{-3p}=-\frac{3p^3}{3p}+\frac{9p^{2}q}{3p}+\frac{6p{q}^2}{3p}=-\left(\frac{3\times p\times p\times p}{3p}\right)-\left(\frac{3\times 3\times p\times p\times q}{3p}\right)+\left(\frac{2\times 3\times p\times q\times q}{3p}\right)=-p^2+3pq+2q^2$

Hence, $\frac{3p^3-9p^{2}q-6p{q}^2}{-3p}=2q^2+3pq-p^2$.