Answer:
f(x) = [tex]x^{4}[/tex] + 8x² - 9
Step-by-step explanation:
Given the zeros of a polynomial say x = a and x = b, then
the corresponding factors are (x - a) and (x - b)
The polynomial is the the product of the factors
f(x) = (x - a)(x - b)
Given zeros x = 1, x = - 1, x = 3i and x = - 3i, then corresponding factors are
(x - 1), (x + 1), (x - 3i) and (x + 3i), then
f(x) = (x - 1)(x + 1)(x - 3i)(x + 3i) ← expand in pairs using FOIL
= (x² - 1)(x² - 9i²) → note i² = - 1, thus
= (x² - 1)(x² + 9) ← distribute
= [tex]x^{4}[/tex] + 9x² - x² - 9 ← collect like terms
= [tex]x^{4}[/tex] + 8x² - 9
