Question

Write the polynomial function, in standard form, that has zeros -1, -2, and 3.

Answer 1

f(x) = x³ - 7x - 6

Explanation:

Given that the zeros are x = - 1, x = - 2 and x = 3 then the corresponding factors are

(x + 1), (x +2) and (x - 3)

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

f(x) = (x + 1)(x + 2)(x - 3) ← expand the first pair using FOIL

= (x² + 3x + 2)(x - 3) ← distribute

= x³ - 3x² + 3x² - 9x + 2x - 6 ← collect like terms

= x³ - 7x - 6

Answer 2

The sum of the roots of a polynomial is 5/3, the product of the same polynomial is -11. Write the polynomial function in standard form.n: