Question

Is g(x) = (x-1)(x+1)(x-3i)(x+3i) the factored form of f(x) = x^4+8x^2-9

Answer 1

Yes

Explanation:

(x-1)(x+1)(x-3i)(x+3i)

FOIL ( x-1) (x+1) = x^2 -x+x-1 = x^2 -1

FOIL (x-3i)(x+3i) = x^2 +3ix -3ix -9i^2 = x^2 -9(-1) = x^2 +9

(x-1)(x+1)(x-3i)(x+3i) = (x^2 -1) (x^2 +9)

FOIL again

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

x^2 +8x^2 -9

This is the factored form