Math Factoring Help?

Question

I have one really hard problem left on my math homework. To finish it, I need to factor one trinomial, and I can't get it. Can any of you get it? It's:

2x^2+2x-24

I know it probably is simple, but I can't get it!!

Answer 1

It's okay, no one was born knowing everything.

First you have to find out what is the type of factoring you'll use: the kind in here is grouping.

You have to multiply the first and last number os the trinomial: 2 times 24, you got 48. Now you need to find two numbers that can be multiplied and give you 48, and that could also be added or subtracted and give you the number in the center of the trinomial: 2.

In this case, those perfect two numbers are 8 and 6.
You multiply 8 and 6 and you get 48, you subtract 6 from 8 and you get 2.

Now you have that, you get: 2x^2 + 8x - 6x + 4
Now you have four terms you can group them in pairs:
(2x^2 + 8x) - (6x + 4)

Now you must factor my the common factor in each pair:
You get: 2x (x+4) - 6 (x+4)

And finally you're left with: (2x-6) (x+4)

Good luck

PS the answers above are mostly WRONG, I bet my life on it, I'm studying this right now at school...

Answer 2

Here's how you can factor this trinomial:

1) What number/variable(s) can be taken out of the entire polynomial? 2 is the only number that can be removed.
2) Simplify to 2(x^2+x-12). Factor the simplified trinomial. What two numbers, when multiplied equal -12 and added together equal 1? The answer is 4 and -3.
3) Simplify the trinomial to 2(x+4)(x-3).

Here are some additional problems that you can work on to practice the concept:

1) 3x^2 + 6x - 24
2) 2x^2 - 12x + 10
3) 3x^2 - 9x + 6
4) 6x^2 - 20x - 16
5) 4x^2 - 64

E-mail me at [e-mail] if you want the answer key or need help on more advanced factoring. The last one may be a tough one, I will warn you :)

Answer 3

First, factor out the 2, to make things simpler:

2(x^2 + x - 12)

So what are the factors of 12? 1, 2, 3, 4, 6, and 12. Two of those must be in your factored equation. However, added together, these two must ALSO equal one. This seems impossible until you realize that you have a negative in your equation, so if you re-ask the question with which negative and positive numbers added together, what would equal 1, it is easier to spot: -3 and 4

Once you've figured out these factors, it's pretty much done for you.

2(x - 3)(x + 4)

and then to check that it's right, multiply it out and see that you get the same answer.

Answer 4

Start with the 2x and x. Look for factors of 24 (1 and 24, 2 and 12, 3 and 8, 4 and 6) and then look for a pair where one of them divided by 2 (6/2=3) works.

(2x + 8)(x - 3)

Roots of x: x = -4, x = 3

I hope this didn't help you cheat!

Answer 5

factor out the two
2(x^2+x-12)
factor polynomial
2(x+4)(x-3)