SOLUTION: Facor the polynomial. v^2-22v-75

Question 121206: Facor the polynomial. v^2-22v-75
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -75 respectively.

Now multiply the first coefficient 1 and the last coefficient -75 to get -75. Now what two numbers multiply to -75 and add to the middle coefficient -22? Let's list all of the factors of -75:

Factors of -75:
1,3,5,15,25,75

-1,-3,-5,-15,-25,-75 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -75
(1)*(-75)
(3)*(-25)
(5)*(-15)
(-1)*(75)
(-3)*(25)
(-5)*(15)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -22? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -22

First Number	Second Number	Sum
1	-75	1+(-75)=-74
3	-25	3+(-25)=-22
5	-15	5+(-15)=-10
-1	75	-1+75=74
-3	25	-3+25=22
-5	15	-5+15=10

From this list we can see that 3 and -25 add up to -22 and multiply to -75

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 )

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Answer:
So factors to

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