# How do you use the factor theorem to determine whether y-2 is a factor of -4y^3 + 3y^2 – 2y + 1?

May 6, 2018

$y - 2 \text{ is not a factor}$

#### Explanation:

$\text{by the factor theorem for a polynomial } f \left(x\right)$

$\text{if "x-a" is a factor then } f \left(a\right) = 0$

$\text{evaluate for } y = 2$

$\Rightarrow - 4 {\left(2\right)}^{3} + 3 {\left(2\right)}^{2} - 2 \left(2\right) + 1$

$= - 32 + 12 - 4 + 1 = - 23 \ne 0$

$\Rightarrow y - 2 \text{ is not a factor of the polynomial}$