# x^3+kx+7 is divided by (x-2) ....

• Jan 8th 2009, 10:41 AM
coyoteflare
x^3+kx+7 is divided by (x-2) ....
the remainder is 3. find the value of k.

• Jan 8th 2009, 10:53 AM
Moo
Hello,
Quote:

Originally Posted by coyoteflare
the remainder is 3. find the value of k.

We have $P(x)=x^3+kx+7$
So there exists a polynomial $Q(x)$ such that :
$P(x)=Q(x)(x-2)+3$

One simple way to solve it is to let $x=2$
So we have :
$P(2)=Q(2)(2-2)+3=3$

$(2)^3+2k+7=3$

$8+2k+7=3$

$k=\dots$