we the polynomial x^4+kx^2-kx+2 by x+2 the remainder is 36. What"s the value of k?
Hello, gumi!
Are you familiar with the Remainder Theorem?We divide the polynomial $\displaystyle x^4+kx^2-kx+2$ by $\displaystyle x+2$
and the remainder is 36. What is the value of $\displaystyle k$ ?
Given a polynomial $\displaystyle P(x)$, the remainder when dividing by $\displaystyle (x-a)$ is $\displaystyle P(a)$.
The remainder when $\displaystyle x^4 + kx^2 - kx + 2$ is divided by $\displaystyle (x + 2)$ is:
. . $\displaystyle P(\text{-}2) \:=\:(\text{-}2)^4 + k(\text{-}2)^2 - k(\text{-}2) + 2 \:=\:36$
Hence: .$\displaystyle 16 + 4k + 2k + 2 \:=\:36\quad\Rightarrow\quad 6k \:=\:18 \quad\Rightarrow\quad\boxed{k \:=\:3} $