SOLUTION: Hi! What is the process to convert a FOIL expression back into quadratic equation? example: 5p squared + 14pq -3q squared=0 I know that the answer is (5p-q) (p + 3q)

Question 281637: Hi!
What is the process to convert a FOIL expression back into quadratic equation?
example:
5p squared + 14pq -3q squared=0
I know that the answer is (5p-q) (p + 3q)
What are the operations to arrive at the above expression?
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 5 and -3 respectively.

Now multiply the first coefficient 5 and the last coefficient -3 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient 14? Let's list all of the factors of -15:

Factors of -15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 14

First Number	Second Number	Sum
1	-15	1+(-15)=-14
3	-5	3+(-5)=-2
-1	15	-1+15=14
-3	5	-3+5=2

From this list we can see that -1 and 15 add up to 14 and multiply to -15

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

------------------------------------------------------------

Answer:
So factors to

In other words,

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