Question

P(x)=2x^4-x^3+2x^2-kP(x)=2x

Answer 1

Answer:

k=3

Step-by-step explanation:

The given polynomial is

$p(x) = 2 {x}^{4} - {x}^{3} + 2 {x}^{2} - k$

This polynomial is divided by x+1 and the remainder is 2.

We want to find the value of k.

We can find k, using the remainder theorem.

According to the remainder theorem, when p(x) is divided by x+a, the remainder is given by p(-a).

So

$p( - 1) = 2$

This implies that:

$2 {( - 1)}^{4} - {( - 1)}^{3} + 2 {( - 1)}^{2} - k = 2$

We simplify to get:

$2 + 1 + 2 - k = 2$

$5 - k = 2$

$k = 5 - 2 = 3$

The value of k is 3.

Answer 2

Answer:

k=4

Step-by-step explanation: