# How do you factor b^2 + 6b -27?

May 24, 2015

Given that the term in ${b}^{2}$ has coefficient $1$ and taking into account the signs of the other coefficients, this may factor as:

${b}^{2} + 6 b - 27 = \left(b + m\right) \left(b - n\right)$

$= {b}^{2} + \left(m - n\right) b - m n$

where $m > 0$, $n > 0$, $m - n = 6$ and $m n = 27$.

$27 = 9 \times 3$ and $6 = 9 - 3$

so we can choose $m = 9$, $n = 3$ to get:

${b}^{2} + 6 b - 27 = \left(b + 9\right) \left(b - 3\right)$