Perform the division of the polynomials by monomials. $\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }$
A) $2 p ^ { 4 } + 6 p ^ { 7 } + 5 p ^ { 6 }$
B) $2 p ^ { 2 } + 6 p ^ { 7 } + 5 p ^ { 5 }$
C) $2 p ^ { 2 } + 6 p ^ { 10 } + 5 p ^ { 5 }$

Question

Quizplus · Accepted Answer

To divide by a monomial, we can use the rule that states we can divide each term of the polynomial by the monomial separately.

\begin{align*}
\frac{18p^6 + 54p^{11} + 45p^9}{9p^4} &= \frac{18p^6}{9p^4} + \frac{54p^{11}}{9p^4} + \frac{45p^9}{9p^4} \
&= 2p^2 + 6p^7 + 5p^5
\end{align*}

Therefore, the answer is B, and we can check that it is correct by multiplying it by 9p^4 and seeing that it gives us back the original polynomial.

Perform the Division of the Polynomials by Monomials 18p6+54p11+45p99p4\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }9p418p6+54p11+45p9​

Perform the Division of the Polynomials by Monomials $\frac { 18 p ^ { 6 } + 54 p ^ { 11 } + 45 p ^ { 9 } } { 9 p ^ { 4 } }$