# How do you write x^2-x-42 in factored form?

Sep 16, 2015

color(blue)((x+6)(x-7) is the factorised form of the expression.

#### Explanation:

x^2−x−42

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

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 42 = - 42$
AND
${N}_{1} + {N}_{2} = b = - 1$

After trying out a few numbers we get ${N}_{1} = - 7$ and ${N}_{2} = 6$
$- 7 \cdot 6 = - 42$ and $- 7 + 6 = - 1$

x^2−x−42=x^2−7x+6x−42

$= x \left(x - 7\right) + 6 \left(x - 7\right)$

=color(blue)((x+6)(x-7)