Find a polynomial with a degree of 3, and the zeros 1,7, & -4 with no other zeros.

f(x) = x³ - 4x² - 25x + 28

Step-by-step explanation:

Given the zeros x = 1, x = 7 and x = - 4 , then the corresponding factors are

(x - 1), (x - 7), (x + 4)

The polynomial is then the product of the factors, that is

f(x) = a(x - 1)(x - 7)(x + 4) , a is a multiplier

let a = 1 and expand the first pair of factors using FOIL

f(x) = (x² - 8x + 7)(x + 4) ← distribute

      = x³ - 8x² + 7x + 4x² - 32x + 28 ← collect like terms

      = x³ - 4x² - 25x + 28

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation: