SOLUTION: Factor the trinominal 2(m+p)^2-7(m+p)-30

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Question 214295: Factor the trinominal
2(m+p)^2-7(m+p)-30
Found 2 solutions by solver91311, drj:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Looks uglier than a mud fence. But a simple little substitution will help us tame this beast.

Let , then



Not so bad anymore, hmmm?

We know that we need something that looks like

or

We know this because in order to get as a first term, one binomial has to have and the other must have as the first terms. We also know that the signs in the two binomials must be opposite because the constant term of the trinomial is negative.

We have several choices for factors of -30: -5 and 6, 5 and -6, -3 and 10, 3 and -10, -2 and 15, 2 and -15, -1 and 30, 1 and -30. 2 times one of the factors plus the other factor has to equal -7. Looking over the possibilities, it looks like 2 times -6 is -12 plus 5 is -7, so:

Ah ha!!

Now just substitute back:




John

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the trinominal

2%28m%2Bp%29%5E2-7%28m%2Bp%29-30

Step 1. Let x=m+p, then

2x%5E2-7x-30

Step 1. We need to find two integers A and B that A*B=ac and A+B=b where

ax%5E2%2Bbx%2Bc in order to be factorable and a=2, b=-7 and c=-30

Step 2. In the above example, then A*B=-60 and A+B=-7.

Step 3. After trial and error the numbers are A=-12 and B=5

Step 4. Using step 3, we can use grouping as follows

2x%5E2-7x-30=2x%5E2-12x%2B5x-30 where -7x=-12x%2B5x

2x%5E2-7x-30=%282x%5E2-12x%29%2B%285x-30%29

Step 5. Factor out 2x in first group and 5 in second group

2x%5E2-7x-30=2x%28x-6%29%2B5%28x-6%29

Step 6. Factor out (x-6) since it is common in both groups.

2x%5E2-7x-30=%282x%2B5%29%28x-6%29

We can use the FOIL method to verify

2x%5E2-7x-30=2x%5E2-12x%2B5x-30=2x%5E2-7x-30

Step 6. Now substitute back x=m+p to 2x%5E2-7x-30=%282x%2B5%29%28x-6%29 to get


2%28m%2Bp%29%5E2-7%28m%2Bp%29-30=%282%28m%2Bp%29%2B5%29%28m%2Bp-6%29 (ANSWER)

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J