Choose the one alternative that best completes the statement or answers the question.
Use long division to divide.
-$\frac { 64 x ^ { 3 } + 1 } { 4 x + 1 }$
A) $16 x ^ { 2 } - 4 x + 1$
B) $16 x ^ { 2 } + 1$
C) $16 x ^ { 2 } - 1$
D) $16 x ^ { 2 } + 4 x + 1$

Question

Quizplus · Accepted Answer

Dividing $64x^3 + 1$ by $4x + 1$ using long division, the first term in the quotient is $16x^2$ because $4x \times 16x^2 = 64x^3$. Subtracting $64x^3 + 16x^2$ from $64x^3 + 1$ leaves a remainder of $0$, but since we need to match the original expression exactly, we continue the division process. The correct division process shows that the remainder after subtracting products of $4x + 1$ from $64x^3 + 1$ results in a quotient of $16x^2 - 4x + 1$, making option A correct.

Choose the One Alternative That Best Completes the Statement or Answers