Question

Find a polynomial f(x) of degree 3 that has the following zeros. -5, 8, 2 Leave your answer in factored form

Answer 1

f(x) = (x + 5)(x - 8)(x - 2)

Explanation:

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

(x - a) and (x - b)

The polynomial is a product of the factors, that is

f(x) = (x - a)(x - b)

Here the zeros are x = - 5, x = 8, x = 2, then corresponding factors are

(x - (- 5)), (x - 8), (x - 2) , that is

(x + 5), (x - 8), (x - 2) and the polynomial is

f(x) = (x + 5)(x - 8)(x - 2)

Answer 2

f(x) = (x+5)(x-8)(x-2)

Explanation:

If we know the zeros, the polynomial is of the form

f(x) = (x-a)(x-b)(x-c) where a,b,c are the zeros

f(x) = (x - -5)(x-8)(x-2)

f(x) = (x+5)(x-8)(x-2)