How do you factor $x^2 - 2x - 8$ ?

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Answer 1 · 2015-06-10T17:36:42

$color(blue)((x+2)(x - 4)$

$x^2 - 2x - 8$

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

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

$N_1*N_2 = a*c = 1*(-8) = -8$
and
$N_1 +N_2 = b = -2$

After trying out a few numbers we get $N_1 = -4$ and $N_2 =2$
$-4*2 = -8$ , and $2+(-4)= -2$

$x^2 - 2x - 8 = x^2 - 4x +2x - 8$
$=x(x - 4) +2(x - 4)$
$=color(blue)((x+2)(x - 4)$

How do you factor x^2 - 2x - 8x^2 - 2x - 8?