# How do you use the factor theorem to determine whether x-2 is a factor of f(x) = 2x³-9x²+7x+6?

Jan 7, 2016

f(2) = 0 or divide $2 {x}^{3} - 9 {x}^{2} + 7 x + 6$ by (x - 2)
using synthetic division.

#### Explanation:

check using f(2)

$f \left(2\right) = 2 \times {2}^{3} - 9 \times {2}^{2} + 7 \times 2 + 6 = 16 - 36 + 14 + 6$

$\Rightarrow f \left(2\right) = 0$

This means that x = 2 is a root and therefore ( x - 2 ) is a factor.