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

Aug 29, 2016

The remainder is $- 100$.

#### Explanation:

According to remainder theorem if a polynomial function $f \left(x\right) = {a}_{0} + {a}_{1} x + {a}_{2} {x}^{2} + {a}_{3} {x}^{3} + \ldots . + {a}_{n} {x}^{n}$ is divided by $\left(x - a\right)$, the remainder is given by $f \left(a\right)$.

Hence, as $f \left(x\right) = 2 {x}^{3} - 11 {x}^{2} + 17 x - 6$ 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

= $- 16 - 44 - 34 - 6$

= $- 100$