Question

what are the factors of x^4-81

Answer 1

(x^2 - 9) and (x^2 + 9) are factors of x^4 - 81

We can verify this by multiplying them.

(x^2 - 9)(x^2 + 9)

x^4 + 9x^2 - 9x^2 - 81

x^4 - 81

When we have a binomial with two perfect squares, we can use this equation:

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