Question

How do you use the remainder theorem to determine the remainder when the polynomial `2x^3+3x^2-5x+2` is divided by `x+2`?

Answer 1

`8`

Explanation:

The remainder theorem states that a polynomial `P(x)` is divided by `(x-a)` the remainder is `P(a)`

so for `P(x)=2x^3+3x^2-5x+2`

the remainder on dividing by `(x+2) " is " P(-2)`

`P(-2)=2(-2)^3+3(-2)^2-5(-2)+2`

`P(-2)=2xx-8+3xx4+10+2`

`P(-2)=-16+12+10+2=8`