Question

The remainder when p\left(x\right)=x^3-2x^2+8x+kp ( x ) = x 3 − 2 x 2 + 8 x + k by (x-2) is 19. What is the remainder when p(x) is divided by (x+2)?

Answer 1

k=51

Explanation:

Recall from the remainder theorem that, when a polynomial p(x) is divided by (x+a), the remainder is given by;

`p( - a)`

The given polynomial is

`p(x) = {x}^(3) - 2 {x}^(2) + 8x + k`

and the divisor is x+2.

The remainder is given by:

`p( - 2) = {( - 2)}^(3) - 2 {( - 2)}^(2) + 8( - 2) + k = 19`

Simplify;

`- 8 - 8 - 16+ k = 19`

`-32+ k = 19`

`k = 19 + 32`

`k = 51`