Question

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

Answer 1

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

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)`