Use synthetic division to divide.
-$$\left( x ^ { 4 } + 625 \right) \div ( x - 5 )$$
A) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 625 } { x - 5 }$
B) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$
C) $x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125 + \frac { 1250 } { x - 5 }$
D) $x ^ { 3 } - 5 x ^ { 2 } + 25 x - 125 + \frac { 1250 } { x - 5 }$

Question

Quizplus · Accepted Answer

To use synthetic division, write the coefficients of the dividend in order of decreasing exponents, and then bring down the constant. The first number outside the division bracket is the divisor. Then, multiply the divisor by the first term of the dividend, and carry out the addition operation. Then continue the process using the result of this first division step until you have a line with the last dividend term and a remainder. The result of the division is the coefficients of the polynomial quotient, and the remainder over the divisor. 
$$\begin{array}{c|ccccc}
5 & 1 & 0 & 0 & 0 & 625 \
\hline
& & 5 & 25 & 125 & 625 \
\hline
& 1 & 5 & 25 & 125 & \boxed{1250/(x-5)}
\end{array}$$
Thus, the quotient is $x^3+5x^2+25x+125$, and the remainder is $1250/(x-5)$. Therefore, the best choice is $\boxed{\textbf{(C) } x^3+5x^2+25x+125+\frac{1250}{x-5}}$.

Use Synthetic Division to Divide (x4+625)÷(x−5)\left( x ^ { 4 } + 625 \right) \div ( x - 5 )(x4+625)÷(x−5)

Use Synthetic Division to Divide $\left( x ^ { 4 } + 625 \right) \div ( x - 5 )$