Question

factoring trinomials?!
10m^2-13mn-3n^2

Answer 1

@kayladavidson Do you know how to factor 10m^2 - 13m - 3 ?
If so, we'll begin there.

Answer 2

Wow, I was about to respond and your answer vaporized.

Answer 3

Well I knew it wasn't right. I've been doing problems like this all night nothing seems to make sense anymore.

Answer 4

Let's step back.

Does factoring x^2 - 5x + 6 seem possible for you to do? You would look for two numbers that multiply to 6 and add to -5.

Answer 5

-6 and 1. I get things like that, but when it's something like the one I'm trying now, I don't understand what can add up to -13 and multiply to -3

Answer 6

I hear you.
First, -6 and 1 do not multiply to 6. They do add to -5.
The numbers you want are -3 and -2.
Then, factor by grouping.
x^2 - 5x + 6 = x^2 - 3x -2x +6
= x(x-3) - 2(x -3) = (x-3)(x-2)
That's the kind of thing we're about to do with the problem you posted.

Answer 7

10m^2-13mn-3n^2
-----------------
Needed: two numbers that multiply to -30 and add to -13 ARE
the following: -15 and +2. Agree?

Answer 8

10m^2-13mn-3n^2 =
10m^2 -15mn + 2 mn - 3n^2
= ?
Do you see how to do the next step?

Answer 9

Factor by grouping?

Answer 10

Yes.

Answer 11

5m(2m-3n)n(2m-3n)
(5m+n)(2m-3n)
?

Answer 12

10m^2-13mn-3n^2 =
10m^2 -15mn + 2 mn - 3n^2 =
5m( 2m - 3n) + n(2m -3n) =
The line above is the grouping.
The object is to get the same factor in each expression.
In this problem, (2m - 3n) is part of both expressions and will factor out.

Answer 13

Will you pick up from here:

5m( 2m - 3n) + n(2m -3n) =

Think about it as factoring a common factor from: 2x + 4y which would give 2(x + 2y). That may or may not help.

Answer 14

(5m+n)(2m-3n)

Answer 15

5m( 2m - 3n) + n(2m -3n) =
(2m - 3n) (5m + n) which is what you have.

Answer 16

Thanks!

Answer 17

Glad to help. It takes time and practice to get the hang of factoring. I recall getting extremely frustrated when I first started to learn how to do it. So, don't give up.