Given f(x) = 2x^2+ kx – 9, and the remainder when f(x) is divided by x + 6 is 57, then what is the value of k?

Given:

The function is

The remainder when f(x) is divided by x+6 is 57.

To find:

The value of k.

Solution:

According to the remainder theorem, if a polynomial function f(x) is divided by (x-a), then f(a) is the remainder.

The remainder when f(x) is divided by x+6 is 57.

Using remainder theorem, we get f(-6)=57.

Putting x=-6 in the given function.

On further simplification, we get

Therefore, the value of k is 1.

a

step-by-step explanation: