one of the factors of 16xpower of 4-1 is 4xsquared +1

Question

a. 8x+1, x-1

b. 4x-1, x+1

c. 2x+1, 2x-1

d. 4x+1, x-1

Answer 1

Maira, if I am reading this right, you are given the following binomial:

16x⁴ - 1

 and you are asked to factor it.

Well, you should recall that, in general, if you are given something like

a⁴-b⁴ 

you can factor it  as follows

a⁴-b⁴ = (a²+b²)(a²-b²).

Now the first term, (a²+b²), cannot be factored anymore, but the second one can be further factored as

(a²-b²) = (a+b)(a-b). Hence, we find:

a⁴-b⁴ = (a²+b²)(a²-b²) = (a²+b²)(a+b)(a-b).

Back to your case: let 16x⁴ = (2x)⁴ be your a⁴ and 1 = 1⁴ be your b⁴  and use the result we just got for a⁴-b⁴.......................

 ^{[You will establish that the only possible correct answer among the alternatives given is (c)]}