Question

Factor the binomial or identify it as prime.

2z4 – 2

A. 2(z2 + 1)(z2 – 1)
B. 2(z2 + 1)(z – 1)(z + 1)
C. Prime
D. 2(z2 + 1)2

Answer 1

the answer to this problem is A
:)

Answer 2

The correct answer is B,

Explanation:

Since the higher value of z's power, is 4, an even number, and the second number is negative, we can think that this binomial is made of a difference of squares, so that is what we are going to factorize.

First, extract the common number (if any), the number 2, we have now>

`2*(z^(4)-1)`

This is convenient since "1" is a wonderful number that has this feature>
`1^(n)= 1` No matters what n's value is,

so the first equation
`2*(z^(4)-1)` can be written as
`(2*(z^(4)-1)=2*((z^(2))^(2)-1^(2))=2*(z^(2)-1)*(z^(2)+1)`

The later termn, can also be factorized, using the same as befre.

`(z^(2)-1)=(z-1)*(z+1)`

Remember that
`z^(4)=(z^(2))^(2)`