How do you factor $x^{2} = x + 2$ $x^2 = x + 2$ ?

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How do you factor $x^{2} = x + 2$ $x^2 = x + 2$ ?

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Answer 1 · 2016-03-23T17:42:51

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

Explanation:

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

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

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

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

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot (- 2) = - 2$ $N_1*N_2 = a*c = 1*(-2) = -2$

AND

$N_{1} + N_{2} = b = - 1$ $N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_{1} = - 2$ $N_1 = -2$ and $N_{2} = 1$ $N_2 =1$
$1 \cdot (- 2) = - 2$ $1*(-2) = -2$ , and $1 + (- 2) = - 1$ $1+(-2)= -1$

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

$= x (x - 2) + 1 (x - 2)$ $= x ( x-2 ) + 1 (x-2)$

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

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

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How do you factor $x^{2} = x + 2$ $x^2 = x + 2$ ?

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Explanation:

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