# How do you factor 5y^2-26y+5?

May 28, 2015

Use a version of the AC method...

$A = 5$, $B = 26$, $C = 5$.

$A C = 5 \times 5 = 25$

since the sign of the constant term is $+$, look for a pair of factors of $A C = 25$ which add to give $26$. $1$ and $25$ work.

Use this pair to split the middle term into two, then factor by grouping...

$5 {y}^{2} - 26 y + 5 = 5 {y}^{2} - 25 y - y + 5$

$= \left(5 {y}^{2} - 25 y\right) - \left(y - 5\right)$

$= 5 y \left(y - 5\right) - \left(y - 5\right)$

$= \left(5 y - 1\right) \left(y - 5\right)$