SOLUTION: I am trying to solve a factoring problem with quadratic trinomials that have a leading coefficient greater than 1. My problem is: (2x^2+14x-10). I am having trouble finding number

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Question 581663: I am trying to solve a factoring problem with quadratic trinomials that have a leading coefficient greater than 1. My problem is: (2x^2+14x-10).
I am having trouble finding numbers that multiply to -20 and add to 14. Help would be great! Thank you!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Start with the given expression.

Factor out the GCF .

Now let's try to factor the inner expression

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Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,5
-1,-5

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-5) = -5
(-1)*(5) = -5

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number Second Number Sum
1 -5 1+(-5)=-4
-1 5 -1+5=4

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

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Answer:

So simply factors to

In other words, .