# How do you factor: y= s^2-8s+7 ?

Jun 22, 2018

$y = {s}^{2} - 8 x + 7 \Leftrightarrow \textcolor{b l u e}{y = \left(s - 7\right) \left(s - 1\right)}$

#### Explanation:

Since $\left(s + a\right) \left(s + b\right) = {s}^{2} + \left(a + b\right) s + a b$
we are looking for constants $a$ and $b$
such that $a \times b = + 7$
and $\left(a + b\right) = - 8$

Jun 22, 2018

The same processes as when you use $x$

$y = \left(s - 1\right) \left(s - 8\right)$

#### Explanation:

Note that $1 \times 7 = 7 \mathmr{and} 1 + 7 = 8$

but we need negative 8 so we use

$\left(- 1\right) \times \left(- 7\right) = + 7 \mathmr{and} \left(- 1\right) + \left(- 7\right) = - 8$ as required

Thus $y = \left(s - 1\right) \left(s - 8\right)$