SOLUTION: Factor each polynomial completely. If it cannot be factored write "prime" 8x^2+28x-60 I have tried 4(2x^2+8x-15) 4(x+3)(x-5) What do I do now

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Question 90546: Factor each polynomial completely. If it cannot be factored write "prime"
8x^2+28x-60
I have tried 4(2x^2+8x-15)
4(x+3)(x-5)
What do I do now!!
I can't get my -60 to come out when I check it.
Please help!!!!!!!!
Found 2 solutions by jim_thompson5910, bucky:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Start with the given expression.

Factor out the GCF .

Now let's try to factor the inner expression

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Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Factor 8x^2+28x-60
.
Your first step was to take out a factor of 4. This is the correct thing to do. After that
you are left with:
.
4*(2x^2 + 7x - 15)
.
The 2x^2 can only factor to 2x * x so the next step (if 2x^2 + 7x -15 factors) involves:
.
4*(2x ....)*(x ....)
.
the 15 can only factor to 15*1 or 5*3 (ignoring the signs on the two numbers). The potential
factors of 2x^2 + 7x - 15 are therefore:
.
(2x 15)*(x 1)
(2x 1)*(x 15)
(2x 5)*(x 3)
(2x 3)*(x 5)
.
If it factors, there must be some combination with signs between the x terms and the numbers
that adds to +7. Becomes pretty apparent that the factors involving 15 are not likely.
So the most likely factors are (2x 5)*(x 3) or (2x 3)*(x 5).
.
We could have:
.
(2x -5)*(x + 3) but this doesn't work because 2x*3 - 5x = 6x - 5x = +x not +7x
or
(2x + 5)*(x - 3) but this doesn't work because 2x*(-3) + 5x = -6x + 5x = -x not +7x
so if it factors it must be either (2x + 3)*(x - 5) or (2x - 3)*(x + 5). Try:
.
(2x + 3)*(x - 5). The cross products are 2x*(-5) and 3*x = -10x + 3x = -7x. Close, but
the sign is wrong.
.
We are down to trying (2x - 3)*(x + 5). The cross products are 2x*5 and -3*x which lead
to 10x - 3x = +7x. That's what we are looking for. So multiplying out the factors:
.
(2x - 3)*(x + 5) gives 2x*x + 2x*5 -3*x -3*5 = 2x^2 + 6x - 5x -15 = 2x^2 +7x - 15.
Hooray! Now we can say that 2x^2 + 7x - 15 factors to (2x - 3)*(x + 5) and as a result the
whole factoring process results in:
.
4*(2x - 3)*(x + 5)
.
That's the answer and if you multiply this out the product will be the original polynomial
you were given to factor.
.
Factoring like this involves a lot of judgment, guessing, and trial-and-error as you can
see from the above analysis. The more you work these kind of problems the better you will
become at getting to the answer quicker because you will develop a "feel" for what
combinations are more likely to work and what combinations are likely to lead to a
wrong answer.
.
Hope you can follow the above process ... especially with regard to using the cross
products (multiplying a term containing x by a term that is just a number) to look for
a factor that works.
.
And hope that the answer above points out where you made a few simple mistakes in your
logic that led you to an answer that wouldn't check.