Question

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

Answer 1

Remainder Theorem says the remainder in a synthetic division will be `f(k) = f(2) =-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
4. Add the two rows.
5. Repeat steps 3 & 4 until finished.
6. The last sum is the remainder `-206`