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. PrimeD. 2(z2 + 1)2

Answer:The correct answer is B,Step-by-step 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>[tex]2*(z^{4}-1)[/tex]This is convenient since "1" is a wonderful number that has this feature>[tex]1^{n}= 1[/tex] No matters what n's value is, so the first equation [tex]2*(z^{4}-1)[/tex] can be written as [tex](2*(z^{4}-1)=2*((z^{2})^{2}-1^{2})=2*(z^{2}-1)*(z^{2}+1)[/tex]The later termn, can also be factorized, using the same as befre.[tex](z^{2}-1)=(z-1)*(z+1)[/tex]Remember that [tex]z^{4}=(z^{2})^{2}[/tex]