Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement.
-$- 21 s ^ { 7 } + 56 s - 77$
A) $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } - 77 s } { 7 s }$
B) $\frac { - 21 s ^ { 9 } + 56 s ^ { 3 } - 77 s ^ { 2 } } { - 7 s }$
C) $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } + 77 s } { - s }$
D) $\frac { 21 s q - 56 s ^ { 2 } q ^ { 2 } - 77 s ^ { 8 } q ^ { 9 } } { - s q }$
E) $\frac { - 21 s ^ { 8 } q ^ { 8 } + 56 s ^ { 9 } q ^ { 8 } - 77 s ^ { 8 } q ^ { 9 } } { 7 s q }$

Question

Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement.
-$- 21 s ^ { 7 } + 56 s - 77$ 
A) $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } - 77 s } { 7 s }$ 
B) $\frac { - 21 s ^ { 9 } + 56 s ^ { 3 } - 77 s ^ { 2 } } { - 7 s }$ 
C) $\frac { 21 s ^ { 8 } - 56 s ^ { 2 } + 77 s } { - s }$ 
D) $\frac { 21 s q - 56 s ^ { 2 } q ^ { 2 } - 77 s ^ { 8 } q ^ { 9 } } { - s q }$ 
E) $\frac { - 21 s ^ { 8 } q ^ { 8 } + 56 s ^ { 9 } q ^ { 8 } - 77 s ^ { 8 } q ^ { 9 } } { 7 s q }$

Quizplus · Accepted Answer

To divide by a monomial, we need to divide each term of the polynomial by the monomial. Since we are dividing by $-s$, we need to divide each term by $-s$. This gives us: 
\begin{align*}
\frac{-21s^7+56s-77}{-s} &= \frac{-21s^7}{-s} + \frac{56s}{-s} - \frac{77}{-s} \
&= 21s^6 - 56s^2 + \frac{77}{s}
\end{align*}
Matching this with the given choices, we see that only option C has the same polynomial.

Perform the Indicated Divisions of Polynomials by Monomials −21s7+56s−77- 21 s ^ { 7 } + 56 s - 77−21s7+56s−77

Perform the Indicated Divisions of Polynomials by Monomials $- 21 s ^ { 7 } + 56 s - 77$