the remainder is 3. find the value of k.
thanks in advanced
Hello,
We have $\displaystyle P(x)=x^3+kx+7$
So there exists a polynomial $\displaystyle Q(x)$ such that :
$\displaystyle P(x)=Q(x)(x-2)+3$
One simple way to solve it is to let $\displaystyle x=2$
So we have :
$\displaystyle P(2)=Q(2)(2-2)+3=3$
$\displaystyle (2)^3+2k+7=3$
$\displaystyle 8+2k+7=3$
$\displaystyle k=\dots$