How do you use the factor theorem to determine whether x=5 is a root of x^4-3x^3-9x^2-5x=0?

Mar 28, 2018

$x = 5 \text{ is a root}$

Explanation:

$\text{if x = 5 is a root then if "f(5)=0" x = 5 is a root}$

$\Rightarrow {\left(5\right)}^{4} - 3 {\left(5\right)}^{3} - 9 {\left(5\right)}^{2} - 5 \left(5\right)$

$= 625 - 375 - 225 - 25 = 0$

$\Rightarrow x = 5 \text{ is a root}$