Pre-Calculus

Question

Construct a polynomial function with the following properties: fifth degree, 3
3
is a zero of multiplicity 3
3
, −4
−
4
is the only other zero, leading coefficient is 3
3
.

Answer 1

If it is a degree 5 polynomial, it must have 5 roots (either real or imaginary).  You have only listed 4 roots: 3 (mult 3) and -4.  You need a 5th root to proceed

Upon further reflection, they probably mean that -4 has a multiplicity of 2 since it is the only other root. Therefore your polynomial would be 3(x-3)^3(x+4)^2