Question

Can someone simplify 3x^2 +5x-2 and show the steps? I think I'm making a mistake.

Answer 1

There is nothing to simplify. Since there are no like terms, no terms can be combined together.
Do you mean factor the polynomial?

Answer 2

factor yes sorry

Answer 3

3x^2+6x-x-2
3x(x+2)-1(x+2)
(x+2)(3x-1)=0
x=-2 and x=1/3

Answer 4

3 can be factored into 3 and 1.
-2 can be factored into -2 and 1 or -1 and 2.
Because there aren't many ways of factoring 3 and -2, you can try factoring by trial and error.

The 3 of 3x^2 will give you 3 and 1, so you start by writing
(3x )(x )

Now we need to place the factors of -2.
Each set of factors can be placed two ways.

Answer 5

Thats how far I got. Then I tried (3x+2)(x-1)

But that did work because I need to get that 5x and the middle. So then I did (3x+2)(x+1) But I cant get a -2 that way

Answer 6

hey write 5x = 6x-x

Answer 7

and solve

Answer 8

Let's start with -2 and 1.

We can place them as
(3x - 2)(x + 1)
and (3x + 1)(x - 2)
To see if either of these two factorizations is correct, we multiply them out using FOIL.

(3x - 2)(x + 1) = 3x^2 + 3x - 2x - 2 = 3x^2 + x - 2 (This is not it, as the middle term is not correct.)
(3x + 1)(x - 2) = 3x^2 - 6x + x - 2 = 3x^2 -5x - 2 (this is also not it as the middle term is again not correct.)

Answer 9

I did both of those and got the same thing. So is it even factorable?

Answer 10

yup why not?

Answer 11

Now we try with the factors -1 and 2.

Once again there are two possibilities:
(3x - 1)(x + 2)
and (3x + 2)(x - 1)

Now we multiply both out using FOIL to see which one will give us the correct middle term, 5x.

(3x - 1)(x + 2) = 3x^2 + 6x - x - 2 = 3x^2 + 5x - 2 (This is the answer. You can stop here.)

For completeness, I'll multiply out the other possibility to show you that the middle term will not come out 5x.
(3x - 1)(x + 2) = 3x^2 - 3x + 2x - 2 = 3x^2 - x - 2 (as you can see, the middle term does not work out.)


The answer is
3x^2 + 5x - 2 = (3x - 1)(x + 2)

Answer 12

I get it now! Thank you so much for the help.

Answer 13

Remember, for each set of factors of -2, you need to try it both ways.
In this problem, trial and error is not too long since there are only a total of 4 combinations that need to be tested. For other problems, there may be many more combinations, then trial and error is too long. In that case, factoring by grouping is better since it reduces the number of guesses.

Answer 14

You're welcome.

Answer 15

If you want to see the other method, I can show you here with this same problem.