Question

Given the function f ( x ) = 5 x 2 − 5 x 3 . calculate the following values using synthetic division and the remainder theorem: f ( − 2 ) =

Answer 1

To calculate f(-2) using synthetic division and the remainder theorem, substitute -2 into the function f(x) = 5x2 - 5x3. Using synthetic division, the remainder is 25, so f(-2) = 25.

Step-by-step explanation:

To calculate f(-2) using synthetic division and the remainder theorem, we substitute -2 into the function f(x) = 5x2 - 5x3.

Using synthetic division, we set up the division as follows:

-2 | 0 5 -5
| 0 -10 30
__________
0 -10 25

The remainder is the last value in the bottom row, which is 25. Therefore, f(-2) = 25.