Question

Is x − 8 a factor of the function f(x) = −2x3 + 17x2 − 64? Explain. (2 points)

Answer 1

x-8 is a factor of f(x)

Explanation:

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

We are given the function

`f(x)=-2x^3+17x^2-64`

And it's required to find if x-8 is a factor of f.

Applying the mentioned theorem, we only have to find f(8):

`f(8)=-2\cdot 8^3+17\cdot 8^2-64`

Operating:

`f(8)=-2\cdot 512+17\cdot 64-64`

`f(8)=-1024+1088-64`

`f(8)=0`

Thus, x-8 is a factor of f(x)