Question

Is x^2-4 a prime polynomial?

Answer 1

Hint:

a^2 - b^2 = (a-b)(a+b)

by the difference of squares rule

Answer 2

So its not?

Answer 3

Oh wait it is ?

Answer 4

can you write x^2-4 in the form a^2 - b^2

Answer 5

no you cant

Answer 6

are you sure?

Answer 7

you cant make -4 into -b^2 unless you turn it to 2^2 ?

Answer 8

-2^2

Answer 9

4 = 2^2

So

x^2 - 4

becomes

x^2 - 2^2

Answer 10

so we actually can rewrite x^2 - 4 into a^2 - b^2 form

Answer 11

where in this case, a = x and b = 2