Question

Factor this polynomial completely: x4– 25.

Answer 1

(x^2+5)(x^2-5)

Answer 2

difference of two squares:
\[a^2-b^2=(a+b)(a-b)\]
here
\[a=x^2\]
\[b=5\]
so get
\[(x^2+5)(x^2-5)\]

Answer 3

\[x^2+5\] does not factor, but \[x^2-5\] does as \[(x+\sqrt{5})(x-\sqrt{5})\]