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 )
(