SOLUTION: Factor; if cant, write prime: 64p^2 - 63p + 16 (no equal sign by the way) just factor

Question 577749: Factor; if cant, write prime: 64p^2 - 63p + 16 (no equal sign by the way) just factor
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 :
1,2,4,8,16,32,64,128,256,512,1024
-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 = 1024
2*512 = 1024
4*256 = 1024
8*128 = 1024
16*64 = 1024
32*32 = 1024
(-1)*(-1024) = 1024
(-2)*(-512) = 1024
(-4)*(-256) = 1024
(-8)*(-128) = 1024
(-16)*(-64) = 1024
(-32)*(-32) = 1024

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.

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

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

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