In order to factor , first multiply the leading coefficient 3 and the last term 5 to get 15. Now we need to ask ourselves: What two numbers multiply to 15 and add to 8? Lets find out by listing all of the possible factors of 15
-1,-3,-5,-15, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 15.
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8
We can see from the table that 3 and 5 add to 8. So the two numbers that multiply to 15 and add to 8 are: 3 and 5
So the original quadratic
breaks down to this (just replace with the two numbers that multiply to 15 and add to 8, which are: 3 and 5)
Group the first two terms together and the last two terms together like this:
Factor a 3x out of the first group and factor a 5 out of the second group.
Now since we have a common term we can combine the two terms.
Combine like terms.
So the quadratic factors to
Notice how foils back to our original problem . This verifies our answer.