Question

Find a polynomial F(x ) of degree 5 that has the following zeros.

8(multiplicity 2) -2, -9, 0
Leave your answer in factored form.
F(x) = ?

Answer 1

f(x) = x(x + 2)(x + 9)(x - 8)²

Explanation:

Given x = h is a zero of f(x) then (x - h) is a factor

If h has multiplicity 2 then the factor is squared , that is (x - h)²

here the zeros are x = 8 of multiplicity 2 , x = - 2, x = - 9, x = 0

then (x - 8)² , (x - (- 2)) , (x - (- 9)) , x - 0 are the factors, that is

(x - 8)² , (x + 2) , (x + 9) and x

f(x) = x(x + 2)(x + 9)(x - 8)² ← in factored form