Question

How to factor: 0 = 2x^2 - 5x + 2
This is what I have so far -
Factor by grouping:
Multiply the first coefficient 2, by the last coefficient 2 2 * 2 = 4
Find the product of 4, and the sum of the middle term
-5 -1 * -4 = 4 and -1 + -4 = -5
Put the two new numbers in place of the middle term in the trinomial:
0 = 2x^2 - 4 - 5 + 2
Split the equation in half and group: x^2 - 4 and -5 + 2
Now I am lost.

Answer 1

You are on the right track, except you have to include the "x" with the "-4":

2x^2 - 4x - x + 2

From there, split that into the first 2 terms as a pair and the second 2 terms as a pair.

Answer 2

Factor out the 2x from the first pair of terms. From there, you will see a common factor in the first 2 terms and in the second 2 terms.

Answer 3

With these 2 hints, where are you now? @haileemackk

Answer 4

Here's a little more help:

(2x^2 - 4x) - (x - 2)

You should get it from there.

Answer 5

So it's x^2 - 4x and -5 + 2?

Answer 6

How do you get that from my hints?

Answer 7

I was just starting from where I left off because I have to be able to explain it. You said to include the x with the -4.

Answer 8

Just read what I posted, all posts in order. You have to get 2 factors of 4 (the 2 x 2) that when added, equal -5. You identified them as -4 and -1. I said that you have to include -4 and -1 as coefficients on "x" and I gave you an expression to work with in my first post. That's where you have to go from, from now. Not the tail-end of your problem statement. I identified where you went off tangent. So, take it from where I corrected your method.

Answer 9

In other words, you replace the -5 with the -4 and the -1.

Answer 10

The -5x becomes -4x and (-1)x or -4x and -x

Answer 11

So then I have (2x^2 - 4x) and - (x - 2)
Then I would distribute?
2x^2(x - 2) -4x(x - 2)
And then solve from there?

Answer 12

post #1, then post #2, then post #4, especially post #4. Your common factor, once you do the factoring I mentioned, will be (x - 2)

Answer 13

What is (2x^2 - 4x) once you factor out into (2x) and another factor? What is that other factor?

Answer 14

Is it 2x(x -2)

Answer 15

Good! And your other pair of terms, the 3rd and 4th terms of my first post are re-written with parentheses in my fourth post and that also has a grouping of (x - 2). (x - 2) is your common factor.

Answer 16

You have 2x(x - 2) and (-1)(x - 2)

So, combine the 2x and (-1)

Answer 17

That would -2x?

Answer 18

a(x + y) + b(x + y) = (a + b)(x + y)

Answer 19

2x(x - 2) and -1(x - 2)

x(x - 2) -2(x - 2)
2x - 2x and -2x + 4

??

Answer 20

No I think I did that wrong. Ill retry.

Answer 21

Ok, you've tried long enough and you have shown heroic effort. So, here's the rest:

2x(x - 2) and (-1)(x - 2)

2x(x - 2) - (x - 2)

(2x - 1)(x - 2)

And that's your end-result answer.

Answer 22

The trick to getting familiar with this is to think of (x - 2) as one symbol (m):

(2x)(m) - m

(2x - 1)(m)

(2x - 1)(x - 2)

Answer 23

Thanks for trying to help, this has just been a difficult one for me! You've helped me understand a bit better, and thank you for having so much patience with me :)

Answer 24

You're a nice person, and I don't want to see anyone struggle, especially nice people. But learning can be a challenge, and I didn't just want to throw out an answer. Just go over everything again and you'll be fine @haileemackk

Answer 25

Thanks so much, I keep going over it and I've been rewriting the equation over and over but I think I'm finally starting to get it.

Answer 26

If you can get 2 factors of 4 (2 x 2) that add to -5, and those are -4 and -1, and get to my first post, you'll be fine.

Answer 27

It has been nice working with you. I know I "stretched" you a little, but that's good. It's the learning process. Just hang in there. I do believe you are getting it. @haileemackk

Answer 28

Thank you :)