# How do you determine the value of k if the remainder is 3 given (x^3+x^2+kx-15) div(x-2)?

Dec 24, 2016

Use the remainder theorem to find $k = 3$

#### Explanation:

Let $f \left(x\right) = {x}^{3} + {x}^{2} + k x - 15$

By the remainder theorem, the remainder when $f \left(x\right)$ is divided by $\left(x - 2\right)$ will be $f \left(2\right)$

So we have:

$3 = f \left(2\right) = 8 + 4 + 2 k - 15 = 2 k - 3$

Add $3$ to both ends to get:

$6 = 2 k$

Divide both sides by $2$ and transpose to get:

$k = 3$