Find a polynomial with a degree of 3 and zeros - 3,3,5

f (x) = x³ - 5x² - 9x + 45

Step-by-step explanation:

Given x = a, x = b are the zeros of a polynomial, then

(x - a), (x - b) are the factors and f (x) is the product of the factors.

Here the zeros are x = - 3, x = 3 and x = 5, thus

(x + 3), (x - 3) and (x - 5) are the factors and

f (x) = (x + 3) (x - 3) (x - 5) ← expand the first pair of factors using FOIL

= (x² - 9) (x - 5) ← distribute

= x³ - 5x² - 9x + 45