Write a polynomial function in standard form with zeros at 5, -4, and 1.

f(x) = x³ - 2x² - 19x + 20

Step-by-step explanation:

Given a polynomial with zeros x = a, x = b then the corresponding factors are

(x - a)(x - b) and the polynomial is then the product of the factors

Given zeros x = 5, x = - 4, x = 1 , then

(x - 5), (x + 4) and (x - 1) are the factors, then

f(x) = (x - 5)(x + 4)(x - 1) ← expand the first pair of factors using FOIL

     = (x² - x - 20)(x - 1) ← distribute

     = x³ - x² - 20x - x² + x + 20 ← collect like terms

     = x³ - 2x² - 19x + 20

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