Question

HELP ME PLEASE!!!!!!

Find the remainder when f(x) is divided by (x - k).
f(x) = 4x3 - 6x2 + 3x + 1; k= -2

Answer 1

The remainder is -61

Explanation:

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

The given polynomial is:

`f(x) = 4x^3 - 6x^2 + 3x + 1`

We need to find the remainder when f(x) is divided by x+2. According to the above-mentioned theorem, we only need to find f(-2) as follows:

`f(-2) = 4(-2)^3 - 6(-2)^2 + 3(-2) + 1`

`f(-2) = 4(-8) - 6(4) - 6 + 1`

`f(-2) = -32 - 24 - 6 + 1=-61`

The remainder is -61