# Given polynomial f(x)=x^3-2x^2-40x-64 and a factor x-8 how do you find all other factors?

Feb 23, 2017

The other factors are $\left(x + 2\right)$ and $\left(x + 4\right)$

#### Explanation:

We perform a synthetic division

$\textcolor{w h i t e}{a a a a}$$8$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$1$$\textcolor{w h i t e}{a a a a}$$- 2$$\textcolor{w h i t e}{a a a a a}$$- 40$$\textcolor{w h i t e}{a a a a a a}$$- 64$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a}$$\textcolor{w h i t e}{a a a a a a a}$$8$$\textcolor{w h i t e}{a a a a a a}$$48$$\textcolor{w h i t e}{a a a a a a a a}$$64$

$\textcolor{w h i t e}{a a a a a a a a a a}$------------------------------------------------------------

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a a}$$1$$\textcolor{w h i t e}{a a a a a}$$6$$\textcolor{w h i t e}{a a a a a a a}$$8$$\textcolor{w h i t e}{a a a a a a a a}$$\textcolor{red}{0}$

The remainder is $= 0$

The quotient is $= {x}^{2} + 6 x + 8$

This is factorised as

${x}^{2} + 6 x + 8 = \left(x + 2\right) \left(x + 4\right)$