Apolynomial that has 4 turning points is multiplied by another polynomial that has 1 zeros. what is the minimum degree of the new polynomial?

The polynomial with 4 turning points has the degree of 4+1 = 5. Whatever number of turning points there are, add 1 and you get the degree.

The degree of the polynomial with one root or zero is 1

When you multiply polynomials, the degrees will add so 5+1 = 6 is the minimum degree of the new polynomial.

The final answer is 6.