In order to factor  , first we need to ask ourselves: What two numbers multiply to -45 and add to 4? 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
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
| First Number | | | Second Number | | | Sum | | 1 | | | -45 | || | 1+(-45)=-44 | | 3 | | | -15 | || | 3+(-15)=-12 | | 5 | | | -9 | || | 5+(-9)=-4 | | -1 | | | 45 | || | (-1)+45=44 | | -3 | | | 15 | || | (-3)+15=12 | | -5 | | | 9 | || | (-5)+9=4 | We can see from the table that -5 and 9 add to 4.So the two numbers that multiply to -45 and add to 4 are: -5 and 9
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
 substitute a=-5 and b=9
So the equation becomes:
(x-5)(x+9)
Notice that if we foil (x-5)(x+9) we get the quadratic again
If we replace the x's with a's we get
So  factors to
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