# How do you determine the value of k if the remainder is 3 given (x^3+4x^2-x+k)div(x-1)?

Dec 16, 2016

$k = - 1$.

#### Explanation:

the remainder theorem states that if a polynomial $p \left(x\right)$ is divided by $x - a$, then the remainder is given by $p \left(a\right)$.

Here, $a = 1$ and the remainder is $3$.

So:

${\left(1\right)}^{3} + 4 {\left(1\right)}^{2} - 1 + k = 3$

$1 + 4 - 1 + k = 3$

$k = - 1$

Hopefully this helps!