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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