Question 179495: im having trouble with this answer and need help
64p^2-63p+16
thank you sooo much
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Do you want to factor?
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 :
1,2,4,8,16,32,64,128,256,512,1024
-1,-2,-4,-8,-16,-32,-64,-128,-256,-512,-1024
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*1024
2*512
4*256
8*128
16*64
32*32
(-1)*(-1024)
(-2)*(-512)
(-4)*(-256)
(-8)*(-128)
(-16)*(-64)
(-32)*(-32)
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 | 1024 | 1+1024=1025 | | 2 | 512 | 2+512=514 | | 4 | 256 | 4+256=260 | | 8 | 128 | 8+128=136 | | 16 | 64 | 16+64=80 | | 32 | 32 | 32+32=64 | | -1 | -1024 | -1+(-1024)=-1025 | | -2 | -512 | -2+(-512)=-514 | | -4 | -256 | -4+(-256)=-260 | | -8 | -128 | -8+(-128)=-136 | | -16 | -64 | -16+(-64)=-80 | | -32 | -32 | -32+(-32)=-64 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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