5. Find a polynomial \( f(x) \) with a leading coefficient of 2 and a zero at -3 with multiplicity 2 and a zero at 4 with multiplicity 3 . Write your answer in complete factored form.

To construct the polynomial \( f(x) \) with the given conditions, we start by expressing the zeros with their respective multiplicities. The zero at -3 has multiplicity 2, so its factor will be \( (x + 3)^2 \). The zero at 4 has multiplicity 3, leading to the factor \( (x - 4)^3 \). Putting it all together, we have the polynomial in factored form as follows: \[ f(x) = 2(x + 3)^2(x - 4)^3 \] This gives us a polynomial with a leading coefficient of 2, which satisfies all the given conditions.