How do you factor $6x^2 + 14x -12$ ?

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Answer 1 · 2015-05-17T23:53:21

This can be done by find its roots. Knowing its roots, you'll be able to factor your equation, as follows:

First, let's solve this using Bhaskara:

$(-14+-sqrt(14^2-4(6)(-12)))/(2*6)$
$(-14+-22)/12$

Roots:
$x=-3$ , which is the same as the factor $x+3=0$
$x=2/3$ , which is the same as the factor $3x-2=0$

Using these factors, we can rewrite the original function:

$6x^2+14x-12=2(3x^2+7x-6)=2(x+3)(3x-2)$

Answer 2 · 2015-05-18T00:28:57

A Different Method.

The answer is $2(3x-2)(x+3)$ .

Problem: Factor $6x^2+14x-12$

Factor out the GCF $2$ .

$2(3x^2+7x-6)$

Factor $3x^2+7x-6$ . The form of this equation is $ax^2+bx+c$ .

Multiply $a*c$ .

$3*-6=-18$

Determine two numbers that when added will equal $b$ , or $7$ , and when multiplied will equal $a*c$ , or $-18$ .

The numbers $9$ and $-2$ fit the pattern. Rewrite the equation with $9x$ and $-2x$ in place of $7x$ .

$2(3x^2+9x-2x-6)$

Factor by grouping.

$2(3x^2+9x)-(2x-6)$

$2(3x(x+3)-2(x+3))$

Factor out the GCF $x+3$ .

$(3x-2)(x+3)$

Complete answer:

$2(3x-2)(x+3)$

How do you factor 6x^2 + 14x -126x^2 + 14x -12?