# Is it possible to factor y= 35x^2 - 22x + 3 ? If so, what are the factors?

May 10, 2016

$y = 35 {x}^{2} - 22 x + 3 = \left(5 x - 1\right) \left(7 x - 3\right)$

#### Explanation:

Use an AC method:

Find a pair of factors of $A C = 35 \cdot 3 = 105$ with sum $B = 22$.

The pair $15 , 7$ works in that $15 \cdot 7 = 105$ and $15 + 7 = 22$

Use this pair to split the middle term and factor by grouping:

$35 {x}^{2} - 22 x + 3$

$= 35 {x}^{2} - 15 x - 7 x + 3$

$= \left(35 {x}^{2} - 15 x\right) - \left(7 x - 3\right)$

$= 5 x \left(7 x - 3\right) - 1 \left(7 x - 3\right)$

$= \left(5 x - 1\right) \left(7 x - 3\right)$