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How do you write $4x^2+2x-12$ in factored form?

1 Answer

Sep 16, 2015

$4x^2+2x-12$
$color(white)("XXXXXX")=color(green)(2)color(red)((2x+3))color(blue)((x-2))$

Explanation:

Extract the obvious constant factor of $2$ to simplify

$color(green)(2)color(orange)((2x^2+x-6))$

Factoring
by looking for integer factors $a$ and $b$ of $2$
and integer factors $c$ and $d$ of $(-6)$
such that
$(ad+bc)x = 1x$

The only integer factors of $2$ are $1xx2$

Integer factors of $(-6)$ are ${(1xx-6),(2xx-3)(-1xx6),(-3xx2)}$

Checking the four possible combinations, we find:
$color(orange)((2x^2+x-6))=color(red)((2x+3))color(blue)((x-2))$

So $4x^2+2x-12$
$color(white)("XXX")=color(green)(2)color(orange)((2x^2+x-6))$
$color(white)("XXX")=color(green)(2)color(red)((2x+3))color(blue)((x-2))$

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