Apolynomial has 5 turning points is multiplied by another polynomial that has 3 zeros. what is the minimum degree of the new polynomial

A turning point is when the gradient changes sign, namely a local maximum or minimum.
An nth degree polynomial can have up to n-1 turning points.

For example, a straight line (first degree polynomial) does not have a turning point, since 1-1=0.
A parabola is a second degree polynomial, therefore it has 2-1=1 turning point.

If a polynomial has 5 turning points, it has a minimum degree of 5+1=6.

When two polynomials are multiplied together, the resulting degree of the product is the sum of the degrees of the original polynomials.

Ithink the answer is d. not sure but don’t answer it.