x^4-6x^2-8x-3
I tried using synthetic division but the graphs of the two were no where close
Hello, xclo0sive!
What does synthetic division have to do with graphs?
Did you notice that $\displaystyle f(\text{-}1) \:=\:0$ ?Factor: .$\displaystyle f(x) \:=\:x^4-6x^2-8x-3$
. . This means $\displaystyle (x+1)$ is a factor of $\displaystyle f(x).$
$\displaystyle \text{We have: }\;f(x) \;=\;(x+1)\underbrace{(x^3 - x^2 - 5x - 3)}_{g(x)}$
Note that $\displaystyle g(\text{-}1) \:=\:0$
. . Hence: $\displaystyle (x+1)$ is a factor of $\displaystyle g(x).$
$\displaystyle \text{We have: }\;f(x) \;=\;(x+1)(x+1)\underbrace{(x^2-2x-3)}_{h(x)} $
Finally, we see that $\displaystyle h(x)$ can be factored.
Therefore: .$\displaystyle f(x) \:=\:(x+1)(x+1)(x+1)(x-3) \:=\:(x+1)^3(x-3)$