How do you factor the expression $x^2 + 4x – 32$ ?

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Answer 1 · 2016-06-19T09:17:28

$color(blue)( (x -4) ( x + 8 )$ is the factorised form of the expression.

$x^2 + 4 x - 32$

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:

$N_1*N_2 = a*c = 1*(-32) = -32$

AND

$N_1 +N_2 = b = 4$

After trying out a few numbers we get $N_1 = 8$ and $N_2 =-4$
$8*(-4) = -32$ , and $8+(-4)= 4$

$x^2 + color(blue)(4 x) - 32 = x^2 + color(blue)( 8 x - 4x) - 32$

$= x ( x + 8 ) - 4 ( x + 8 )$

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

How do you factor the expression x^2 + 4x – 32x^2 + 4x – 32?