Question

How do you find the remainder when `2x^3-11x^2+17x-6` is divided by x+2?

Answer 1

The remainder is `-100`.

Explanation:

According to remainder theorem if a polynomial function `f(x)=a_0+a_1x+a_2x^2+a_3x^3+....+a_nx^n` is divided by `(x-a)`, the remainder is given by `f(a)`.

Hence, as `f(x)=2x^3-11x^2+17x-6` is divided by `x+2`, the remainder will be given by

`f(-2)=2×(-2)^3-11×(-2)^2+17×(-2)-6`

= `2×(-8)-11×4+17×(-2)-6`

= `-16-44-34-6`

= `-100`