Answer
quotient $x^3-10x^2+51x-260$ and remainder $r(x)=\frac{1300}{x+5}$
Work Step by Step
Step 1. The coefficients of the dividend can be identified as $\{1,-5,1,-5,0\}$ and the divisor is $x+5$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{x^4-5x^3+x^2-5x}{x+5}=x^3-10x^2+51x-260+\frac{1300}{x+5}$ with the quotient as $x^3-10x^2+51x-260$ and the remainder as $r(x)=\frac{1300}{x+5}$
