[tex] \frac{( x^{3}-20x+16) }{(x-4)} [/tex]
Use the rational root theorem:
[tex] a_{o} [/tex]=16, [tex] a_{n} [/tex]=1
The dividers of [tex] a_{o} [/tex]: 1,2,4,8,16
The dividers of [tex] a_{n} [/tex]: 1
Therefore, check the following rational numbers: +-[tex] \frac{1,2,4,8,16}{1} [/tex]
[tex] \frac{4}{1} [/tex] is a root of the expression, so factor out x-4
Compute [tex] \frac{ x^{3}-20x+16 }{x-4} [/tex] to get the rest of the equation.
[tex] \frac{(x-4)( x^{2} +4x-4)}{x-4} [/tex]
Cancel the common factor:
[tex] x^{2}+4x-4[/tex] is the final answer
