Answer:
f(x) = [tex]x^{4}[/tex] + 2x³ - 7x² - 8x + 12
Step-by-step explanation:
Given the zeros of a polynomial , say x = a, x = b
Then the factors are (x - a), (x - b)
and the polynomial is the product of the factors
Given zeros are x = 1, x = 2, x = - 2, x = - 3 then the factors are
(x - 1), (x - 2), (x + 2), (x + 3), and the polynomial is
f(x) = (x - 1)(x - 2)(x + 2)(x + 3) ← expand pairs of factors using FOIL
= (x² - 3x + 2)(x² + 5x + 6) ← distribute
= [tex]x^{4}[/tex] + 5x³ + 6x² - 3x³ - 15x² - 18x + 2x² + 10x + 12 ← collect like terms
= [tex]x^{4}[/tex] + 2x³ - 7x² - 8x + 12
