SOLUTION: My homework is on factoring trinommials and i dont understand it. one problem i have is (the 2 after the b is squared like i dont know how to square it on here): b2+20b+36=0 and i

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Question 22569: My homework is on factoring trinommials and i dont understand it. one problem i have is (the 2 after the b is squared like i dont know how to square it on here): b2+20b+36=0 and i dont know what to do.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Factoring trinomials.
N.B. You can indicate a square by using the caret (^), thus...x^2 = x-squared.
Example, factor:

When you factor a trinomial such as the one above, you are looking for two binomials that will look like this: (b + m)(b + n) and when you multiply these binomial factors, you will get back the trinomial you started with.
So, what are m and n and how do you find them?
Let's multiply the two binomials (b + m)(b + n) and compare the result with the original trinomial.
Simplify.
compare this with:

You can see that for these two trinomials to be equal, then (m+n) = 20 and mn = 36. That is, you are looking for two integers whose sum is 20 and whose product is 36. Let's try some examples:
4 X 9 = 36 and 4 + 9 = 13 No good!
6 X 6 = 36 and 6 + 6 = 12 No good!
2 X 18 = 36 and 2 + 18 = 20 Bingo! So, m = 2 and n = 18
So, mn = 2(18) = 36 and m+n = 2+18 = 20
Now you can write your two binomial factors (b + m)(b + n) as: