SOLUTION: How do you factor m^2 + 30m - 96

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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 NumberSecond NumberSum
1-961+(-96)=-95
2-482+(-48)=-46
3-323+(-32)=-29
4-244+(-24)=-20
6-166+(-16)=-10
8-128+(-12)=-4
-196-1+96=95
-248-2+48=46
-332-3+32=29
-424-4+24=20
-616-6+16=10
-812-8+12=4



From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.


===============================================================



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

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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