# How do you use the remainder theorem and synthetic division to find k=2; f(x)=-5x^5-5x^3-2x^2+2?

Feb 15, 2017

Remainder Theorem says the remainder in a synthetic division will be $f \left(k\right) = f \left(2\right) = - 206$

#### Explanation:

Using Synthetic Division:

1. Put each coefficient including missing coefficients in the first row
2. Drop the first coefficient down
3. Multiply this coefficient by the multiplier $k = 2$ and place in the second row below the 2nd coefficient
6. The last sum is the remainder $- 206$