Question

#5. Solve using synthetic division If you are not knowledgeable in college algebra, please let me know so I can move along more quickly. Thanks in advance!

Answer 1

578

Step-by-step explanation:

By the remainder theorem, if a polynomial, f(x) is divided by a linear factor x-a, then the remainder of the division is f(a).

`f(x)=3x^5-4x^3-5x^2+2`

To determine f(3) using synthetic division, we find the remainder when f(x) is divided by x-3. i.e.

`(3x^5-4x^3-5x^2+2)/(x-3)`

The synthetic division table is attached below:

Therefore, the value of f(3) is 578.