In order to factor  , first multiply the leading coefficient 1 and the last term 45 to get 45. Now we need to ask ourselves: What two numbers multiply to 45 and add to 18? Lets find out by listing all of the possible factors of 45
Factors:
1,3,5,9,15,45,
-1,-3,-5,-9,-15,-45, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 45.
1*45=45
3*15=45
5*9=45
(-1)*(-45)=45
(-3)*(-15)=45
(-5)*(-9)=45
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 18
| First Number | | | Second Number | | | Sum | | 1 | | | 45 | || | 1+45=46 | | 3 | | | 15 | || | 3+15=18 | | 5 | | | 9 | || | 5+9=14 | | -1 | | | -45 | || | -1+(-45)=-46 | | -3 | | | -15 | || | -3+(-15)=-18 | | -5 | | | -9 | || | -5+(-9)=-14 |
We can see from the table that 3 and 15 add to 18. So the two numbers that multiply to 45 and add to 18 are: 3 and 15
So the original quadratic
breaks down to this (just replace  with the two numbers that multiply to 45 and add to 18, which are: 3 and 15)
 Replace with 
Group the first two terms together and the last two terms together like this:
Factor a 1z out of the first group and factor a 15 out of the second group.
Now since we have a common term  we can combine the two terms.
 Combine like terms.
==============================================================================
Answer:
So the quadratic factors to
Notice how foils back to our original problem . This verifies our answer. |
(
