Question

Factor and find roots.
6x^2+x-1

Answer 1

Find two factors of 1 -6 that add up to 1.

Answer 2

Which would be..?

Answer 3

If you can do that, I can help you to your answer...

Answer 4

Finding those would be factoring it and therefore my answer. My problem is that I'm unable to find them.

Answer 5

I mean factors of -6 that add up to 1.

Answer 6

You wouldn't quite have your answer after that.

Answer 7

Oh, 3 and -2?

Answer 8

Yes. Then split up the middle term using that.
\[6x^2 + 3x - 2x - 1 \implies (6x^2 + 3x) + (-2x - 2)\]Can you factor out the GCF in each of those groupings?

Answer 9

\[(2x^2+x) and (-x-1)\]

Answer 10

Not quite.
\[3x(2x + 1) - (2x + 1)\]Now you can use the distributive property and combine them :)
\[(3x - 1)(2x + 1)\]If it doesn't match up, it's because I had a typo above...
There is you're final answer though :)

Answer 11

So how does the 3x come into play when you use the distributive?

Answer 12

That's what you factor out.
\[(6x^2 + 3x) + (-2x - 1)\]See how you can factor out a 3x and factor out a -1?

Answer 13

So what are the 2 zeros?

Answer 14

The original question asks to factor. Not to find the solutions. If you mean the factors, then it's (3x - 1)(2x + 1)

Answer 15

I forgot to put that into the original question x~x

Answer 16

So you're saying you need to find x?

Answer 17

3x - 1 = 0
3x = 1
x = 1/3

2x + 1 = 0
2x = -1
x = -1/2

x = 1/3, -1/2