Apolynomial that has 4 turning points is multiplied by another polynomial that has 9 zeros. what is the minimum degree of the new polynomial

For a given degree of the polynomial, the number of turning points is given by n-1, where n is the degree of the polynomial. A polynomial that has x number of zeros is a polynomial of degree x. Thus the polynomial that has 9 zeros and 4 turning points, is a polynomial of degree 9.