Perform the indicated divisions of polynomials by monomials. Match each of the expressions with the corresponding polynomial to obtain a true statement.
-$- 21 + 56 s q + 77 s s ^ { 7 } q ^ { 8 }$
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.
-$- 21 + 56 s q + 77 s s ^ { 7 } q ^ { 8 }$ 
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 the given polynomial $- 21 + 56 s q + 77 s s ^ { 7 } q ^ { 8 }$ by a monomial, each term of the polynomial must be divided by the monomial. The correct division that matches the given polynomial is option D, where each term of the polynomial is divided by $- s q$, resulting in $21 s q - 56 s ^ { 2 } q ^ { 2 } - 77 s ^ { 8 } q ^ { 9 }$.

Perform the Indicated Divisions of Polynomials by Monomials −21+56sq+77ss7q8- 21 + 56 s q + 77 s s ^ { 7 } q ^ { 8 }−21+56sq+77ss7q8

Perform the Indicated Divisions of Polynomials by Monomials $- 21 + 56 s q + 77 s s ^ { 7 } q ^ { 8 }$