Question

Factor the following quadratic equation;

`12 {x}^(2) + 22x - 14`

Answer 1

2(3x + 7)(2x - 1)

Explanation:

You can see it a little easier if you take out a common factor of 2

2(6x^2 + 11x - 7)

The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.

Let 6 factor into 2 and 3 and the 7 into 7 and 1

2(3x - 1 )(2x + 7)

Now remove the brackets.

2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.

2(6x^2 + 19x - 7)

So we'll try it again

2(3x + 7)(2x - 1)

2(6x^2 + 14x - 3x - 7) Looks like we have it.

2(6x^2 + 11x - 7)

So the right factors are

2(3x + 7)(2x - 1)