SOLUTION: Factor - a2 + 4a - 45

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Question 76764: Factor -
a2 + 4a - 45
Found 2 solutions by Poohbear272, jim_thompson5910:
Answer by Poohbear272(22)   (Show Source): You can put this solution on YOUR website!



Good Luck!
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
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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