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Aerineth(OD)

Factoring Trinomials

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Ok, so Tris and I were working on some Algebra stuff tonight.. and I'm usually pretty good at math.. but it's getting a little tough for me. Now factoring is easy peezy for the most part. I'm curious how any of you do the factoring, as my professor said there's a few different methods of doing them, but she only taught us one. Maybe one of your methods will be easier for me?

The way she taught us, was basically, take you're trinomial you're going to factor, and 'cut and try' to get a foil equation to equal your trinomial. For instance.

36m2 - 60m + 25

Factoring down, you get the factors of both 36 and 25. 36 is 1 and 6, 2 and 13, 3 and 12, 4 and 9, 6 and 6. and 25 is 1 and 25 and 5 and 5. She taught us to randomly pick these factors and place them into your foil equation to get your answer. Randomly choose between the factors until you get a foil that equals the equation.

(6m - 5)2

(6m - 5) (6m - 5)

Both are of course the same equation.. (it's also the correct answer for the specific problem)

My question is.. what are other methods of getting to the correct answer, as she mentioned other methods. This is the method I know.. and it's kind of long. There's got to be an easier (and faster) method, right?

Edited by Aerineth(OD)

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I think this might be exactly the same as your method, but in the form of ax^2 +bx + c I learned that the factor of c * a = b.

So in terms of 36m^2 -60m + 25 you should find the factors of 36 and 25 that multiply and add up to 60. (5*6)(2) = 60

I think this is faster than randomly choosing each and every factor especially when the numbers get big...

There probably are easier methods but math has never been my favorite subject... so sorry if I am not much help.

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Tris pointed me in the direction of a video on youtube. After watching it, it explained what's known as the Berry Method. For me.. it was.. MUCH easier. It goes as such.

36m2 - 60m + 25
(36m - ) ( 36m - )

Bring down your first coefficient. Then multiply the first coefficient (before the first variable) with your last (the one without a variable).

36 * 25 = 900 (This one's a little big but the idea's still the same.)

Take the factors of 900.

1 900

2 450

3 300

4 225

5 180

6 150

9 100

10 90

12 75

15 60

18 50

20 45

25 36

30 30

Now, of the factors of 900, you find the one that (in this case since you need 2 that add together to get a -60 and multiply to get a + number they'll both be negative, hence the sign changes.) Take 30 and 30.

(36m - 30) ( 36m - 30)

Now factor both of them.

6(6m - 5) 6 (6m - 5)

Drop the factor leaving

(6m - 5) (6m - 5)

For me I found this so much easier. Obviously it's much easier with smaller numbers.. but that's the idea.

Also I might add.. this equation would be easier by going with the difference of squares.. but this method will work for trinomial's in general.

Edited by Aerineth(OD)

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calculater app >

kidding only way i know is to jsut factor that down.

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At least for that problem, I would have not broken it down as much.

The best part about 36m2 - 60m + 25 is that two of the coefficients are perfect squares so you know right off the bat that it has to be something like this

(6m (+ or -) 5) (6m (+ or -) 5 )

Now once you figure that you, realizing that the two perfect squares are positive;while 60 is negative that the two signs have to be negative.

Concluding

(6m - 5) (6m-5)

but your way also works; whichever is easier for you.

To me it's easy that way, obviously when you get into different problems that are possibly like 6w² + w - 2 there might be a bit of trial and error.

Now if we were to solve this problem, I first like to figure out the first part which is 6w² which they factors are 6,1 and 2,3 and there's a slim chance it will be 6,1 so then I choose 2 and 3

(3w (2w

Now after you figure that out, then I tackle the last number -2 which its factors are obviously 2 and 1

I think, which factors of 2 times the two values I have split up from 6w² would give me a 1w

well 3w times a -1 would give me a -3w and the 2w times a positive 2 would give me a 4w then added would be w, so that takes care of that part.

so the problem is (3w +2) (2w-1)

I did pretty well at these Aerineth, so if you have questions I don't mind answering them or explaining them.

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uhhhhh 1+1=2 ?????

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I think this might be exactly the same as your method, but in the form of ax^2 +bx + c I learned that the factor of c * a = b.

So in terms of 36m^2 -60m + 25 you should find the factors of 36 and 25 that multiply and add up to 60. (5*6)(2) = 60

I think this is faster than randomly choosing each and every factor especially when the numbers get big...

There probably are easier methods but math has never been my favorite subject... so sorry if I am not much help.

I think this is the easiest way to factor as well... it's just shitty that your teach is using big numbers lol.

ax^2 + bx + c

a * c = n

Find two numbers that add up to b and multiply to n

Using your 36m^2 - 60m + 25 example:

36 * 25 = 900

(-30) + (-30) = (-60); (-30)*(-30) = 900

36m^2 -30m -30m +25 - replace the 60m with the 2 numbers that add up to 60 and mulitply to 900

6m(6m-5) -5(6m-5) - Group the terms and factor. The numbers that are left in the bracket should be the same and are one of the binomials. The numbers outside of the brackets are the other binomial pair.

(6m-5)(6m-5) = final answer.

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