Question 385276: Not understanding, can anyone help?
Factor the expression a^2-6ab+96b^2 into a product of binomials.
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 coefficient is  .
Now multiply the first coefficient by the last coefficient 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=97 | | 2 | 48 | 2+48=50 | | 3 | 32 | 3+32=35 | | 4 | 24 | 4+24=28 | | 6 | 16 | 6+16=22 | | 8 | 12 | 8+12=20 | | -1 | -96 | -1+(-96)=-97 | | -2 | -48 | -2+(-48)=-50 | | -3 | -32 | -3+(-32)=-35 | | -4 | -24 | -4+(-24)=-28 | | -6 | -16 | -6+(-16)=-22 | | -8 | -12 | -8+(-12)=-20 |
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
Also, feel free to check out my tutoring website
Jim
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