How do you factor x^2 = x + 2 ?

Mar 23, 2016

color(green)( (x +1 ) ( x-2 )  is the factorised form of the expression.

Explanation:

${x}^{2} = x + 2$

${x}^{2} - x - 2 = 0$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 2\right) = - 2$

AND

${N}_{1} + {N}_{2} = b = - 1$

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

${x}^{2} - x - 2 = {x}^{2} - 2 x + 1 x - 2$

$= x \left(x - 2\right) + 1 \left(x - 2\right)$

$\left(x - 2\right)$ is a common factor to each of the terms

 =color(green)( (x +1 ) ( x-2 )