# How do you divide (x^3-10x^2+30x+3)/(x-5)?

Nov 14, 2015

Use long division or synthetic division.

#### Explanation:

First step: Realize that $x$ needs to be multiplied by ${x}^{2}$ in order to be the ${x}^{3}$ in ${x}^{3} - 10 {x}^{2} + 30 x + 3$. Then, multiply the ${x}^{2}$ throughout $x - 5$ to get ${x}^{3} - 5 {x}^{2}$ and SUBTRACT it (remember, the signs will change) from ${x}^{3} - 10 {x}^{2} + 30 x + 3$.

You are left with $- 5 {x}^{2} + 30 x + 3$, but only the first term is important for now. Like you did with the ${x}^{3}$ in the first step, realize that you will need to add a $- 5 x$ on top so that the $x \left(- 5 x\right) = - 5 {x}^{2}$. Continue multiplying and subtracting until you get to 28, which is the remainder.

All together, the answer would be written as:
color(blue)(x^2-5x+5+28/(x-5)