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

Answer:

k=51

Step-by-step 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;

$- 8 - 8 - 16+ k = 19$

$-32+ k = 19$

$k = 19 + 32$

$k = 51$