Question 540467: How do you factor m^2 + 30m - 96
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at the expression  , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,8,12,16,24,32,48,96
-1,-2,-3,-4,-6,-8,-12,-16,-24,-32,-48,-96
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-96) = -96
2*(-48) = -96
3*(-32) = -96
4*(-24) = -96
6*(-16) = -96
8*(-12) = -96
(-1)*(96) = -96
(-2)*(48) = -96
(-3)*(32) = -96
(-4)*(24) = -96
(-6)*(16) = -96
(-8)*(12) = -96
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -96 | 1+(-96)=-95 | | 2 | -48 | 2+(-48)=-46 | | 3 | -32 | 3+(-32)=-29 | | 4 | -24 | 4+(-24)=-20 | | 6 | -16 | 6+(-16)=-10 | | 8 | -12 | 8+(-12)=-4 | | -1 | 96 | -1+96=95 | | -2 | 48 | -2+48=46 | | -3 | 32 | -3+32=29 | | -4 | 24 | -4+24=20 | | -6 | 16 | -6+16=10 | | -8 | 12 | -8+12=4 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So doesn't factor at all (over the rational numbers).
So is prime.
If you need more help, email me at jim_thompson5910@hotmail.com
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Jim
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