# How do you solve 35k^2 - 22k + 7 = 4 by factoring?

Aug 7, 2015

Factor: $y = 35 {k}^{2} - 22 k + 7 = 4$

Ans: (5x - 1)(7x - 3)

#### Explanation:

$y = 35 {k}^{2} - 22 k + 3 =$35(x - p)(x - q).
I use the new AC Method to factor trinomials.
Converted trinomial $y ' = {k}^{2} - 22 k + 105$. p' and q' have same sign.
Factor pairs of (105) --> ...(3, 35)(5, 21)(7, 15). This sum is 22 -= -b.
Then p' = -7 and q' = - 15.
Therefor, $p = \frac{p '}{a} = - \frac{7}{35} = - \frac{1}{5}$ and $q = - \frac{15}{35} = - \frac{3}{7}$

Factored form: $y = 35 \left(x - \frac{1}{5}\right) \left(x - \frac{3}{7}\right) = \left(5 x - 1\right) \left(7 x - 3\right)$