Question

Choose two trinomials from the list below to factor. Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation.


2x2 + 13x + 15
2x2 + 27x + 13
5x2 − 2x − 7
10x2 − 7x − 3
8x2 − 11x + 3

Answer 1

Which two did you choose and how far have you gotten with them?

Answer 2

I chose 10x^2 and 8x^2, but I am really confused. My lesson says to do it differently than how I know to.

Answer 3

Did you manage to factor them successfully? How is your method different from the lesson method? Is your prof/teach the sort who is okay with you using a different method that the lesson, as long as it is valid?

Answer 4

No, I have to do it the way the lesson says to, but I can't understand it. And no, I couldn't factor them.

Answer 5

If you wanted to know, the lesson says Factoring Trinomials of the Form ax2 + bx + c

Step 1: Check for a GCF.

Step 2: Split the middle term.

Multiply the leading coefficient and the last term of the trinomial.
Find factors of this product that add to give you the coefficient of the middle term.
Rewrite the polynomial with those factors replacing the middle term of the trinomial.
Step 3: Factor by grouping.

Step 4: Check your factors.

Answer 6

So, what does the lesson ask you to do? You are going to get something resembling (cx+c)(cx+c) for both, where the c's are factors of the x^2 coefficient and the constant's factor.

So the first step is to list the factors for the constant and the x^2's coefficient. Let's start with 10x^2. What are the factors of 10, and the factors of -3?

Answer 7

The factors of 10 are 1&10, and 2&5 and the factors of -3 are -1&3 or 1&-3

Answer 8

Great job, and the middle value is -7. So we two pairs like this: one from the first list times one from the second list. Then those two pairs need to add up to -7. See anything?

Answer 9

Not really

Answer 10

Ok, I'll help with this one. If I take a 10 from the first set times a -1 from the second set, I get -10. Now take something from the first set times something from the second set to get 3, since -10+3 = -7.

Answer 11

Do you see the pair that gives a product of 3?

Answer 12

No, where is it?

Answer 13

Okay, 1 from the first set of factors times 3 from the second set. Now we have picked the pairs (10, 1) from the factors of 10 and (3,-1) from the factors of the constant. Does that help you figure out the factorization?

Answer 14

No, not really.

Answer 15

Hmm, look at the first solution 10x^2 - 7x -3 = (10x+3)(x-1) by foiling, and look over this page http://www.algebrahelp.com/lessons/factoring/trinomial/
and what we've discussed and see if you can make progress. I've got to go, but I'll look in on you next time I log in.
Factoring is tough to learn at first but it's *really* important to understand it well for math.

Answer 16

Thanks for the help!