Question

Form a polynomial with zeros:−2 multiplicity 3; 1 multiplicity 2; 3 multiplicity 1;degree 6 You may leave your answer in factored form.

Answer 1

f(x) = (x+2) (x+2)^3 (x-1) (x-6)

Explanation:

The first zero, -2, corresponds to the factor x+2 of the polynomial.

Given that this zero, -2, has multiplicity 3, (x+2)^3 represent the first three factors of the polynomial.

The next factor stems from the zero 1: (x-1).

The next 6 factors stem from the zero 6: (x-6).

Writing the polynomial in factored form, we get:

f(x) = (x+2) (x+2)^3 (x-1) (x-6)