# How do you factor x² - 8x + 7?

Jun 30, 2015

 color(green)((x-1)(x-7 ) is the factorised form.

#### Explanation:

${x}^{2} - 8 x + 7$

We can Split the Middle Term of this expression to factorise it.

In this technique, since we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 7 = 7$
AND
${N}_{1} + {N}_{2} = b = - 8$

After trying out a few numbers we get ${N}_{1} = - 1$ and ${N}_{2} = - 7$
$\left(- 1\right) \cdot \left(- 7\right) = 7$, and $- 1 + \left(- 7\right) = - 8$

${x}^{2} - 8 x + 7 = {x}^{2} \textcolor{g r e e n}{- 1 x - 7 x} + 7$

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

$\left(x - 1\right)$ is a common factor to each of the terms

 color(green)((x-1)(x-7 ) is the factorised form.

Jun 30, 2015

Factor $y = {x}^{2} - 8 x + 7$
The other real root is $\frac{c}{a} = 7$, then, the corresponding factor is