Question

Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

Answer 1

Answer:

The remainder is 55

Step-by-step explanation:

Let

$p(x)= 2 {x}^{4} + {x}^{2} - 10x - 1$

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

The given divisor is x+2, therefore the remainder is given by:

$p( - 2)$

We substitute x=-2 to get:

$p( - 2)= 2 {( - 2)}^{4} + {( - 2)}^{2} - 10( - 2) - 1$

We simplify to obtain:

$p( - 2)= 2 \times 16 + 4 + 20- 1$

We multiply to get:

$p( - 2)=3 2 + 4 + 20- 1 = 55$

Therefore the remainder is 55