Question

How do you use the remainder theorem to find the remainder when `2x^3 – x^2 – 3x + 7` is divided by x + 2?

Answer 1

The remainder is `-7`

Explanation:

The Remainder Theorem tell us that when polynomial `P(x)` is divided by `x-c`, the remainder is `P(c)`.

When `P(x) = 2x^3 – x^2 – 3x + 7` is divided by `x + 2`,

we are dividing by `x-(-2)`, so the remainder will be:

`P(-2) = 2(-2)^3 – (-2)^2 – 3(-2) + 7`

`= -16-4+6+7 = -20 + 13 = -7`