Question

Use synthetic division and the remainder theorem to find f(4) if f(x) = -2x³+ 9x² -6x + 7

Answer 1

To find f(4) for the polynomial f(x) = -2x³ + 9x² - 6x + 7, synthetic division with 4 is utilized, resulting in a remainder of -9. Hence, f(4) is -9, as per the Remainder Theorem.

Step-by-step explanation:

To find f(4) for the given polynomial function f(x) = -2x³ + 9x² - 6x + 7 using synthetic division and the Remainder Theorem, we follow these steps: When we use synthetic division with 4, the setup will look like this:

4 | -2 9 -6 7
| -8 4 -16
----------------
| -2 1 -2 -9
The remainder, which is the value directly under the last coefficient, is -9. Therefore, f(4) = -9.