Is it possible to factor y=3x^2-11x+6? If so, what are the factors?

Jun 12, 2018

$\left(x - 3\right) \left(3 x - 2\right)$

Explanation:

$\text{using the a-c method to factor the quadratic}$

$\text{the factors of the product } 3 \times 6 = 18$

$\text{which sum to " - 11" are " - 9 " and } - 2$

$\text{split the middle term using these factors}$

$3 {x}^{2} - 9 x - 2 x + 6 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \textcolor{red}{3 x} \left(x - 3\right) \textcolor{red}{- 2} \left(x - 3\right)$

$\text{take out the "color(blue)"common factor } \left(x - 3\right)$

$= \left(x - 3\right) \left(\textcolor{red}{3 x - 2}\right)$

$3 {x}^{2} - 11 x + 6 = \left(x - 3\right) \left(3 x - 2\right)$