# Thread: divide polyinomial when remainder is given

1. ## divide polyinomial when remainder is given

we the polynomial x^4+kx^2-kx+2 by x+2 the remainder is 36. What"s the value of k?

2. Originally Posted by gumi
we the polynomial x^4+kx^2-kx+2 by x+2 the remainder is 36. What"s the value of k?
Synthetically divide and you will get a remainder in terms of k and then you will need to solve $f(k)=36$

3. so K= 3

Is this right?

4. Originally Posted by gumi
so K= 3

Is this right?
I got k=6....to verify rewrite it assuming k=3 to get $f(x)=x^4+3x^2-3x+2$ and divide by x+2

Just to check two common mistakes you did use -2 as your divisor and you did remember to have 5 spaces not four since there is a 0 space for the cubic term?

5. Hello, gumi!

We divide the polynomial $x^4+kx^2-kx+2$ by $x+2$
and the remainder is 36. What is the value of $k$ ?
Are you familiar with the Remainder Theorem?

Given a polynomial $P(x)$, the remainder when dividing by $(x-a)$ is $P(a)$.

The remainder when $x^4 + kx^2 - kx + 2$ is divided by $(x + 2)$ is:

. . $P(\text{-}2) \:=\:(\text{-}2)^4 + k(\text{-}2)^2 - k(\text{-}2) + 2 \:=\:36$

Hence: . $16 + 4k + 2k + 2 \:=\:36\quad\Rightarrow\quad 6k \:=\:18 \quad\Rightarrow\quad\boxed{k \:=\:3}$