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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Is the answer 9?
yes
a polynomial is to be constructed that will touch the x axis at most 7 times . what is the minimum degree of the polynomial please help

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Other answers:

7 for 7 zeros
So the answer is 7? @peachpi
yes
One more please @peachpi
Given the following polynomial find the maximum possible number of turning points f(x)=x^14+x^6+x^9+x^3 @peachpi
max turning point = degree - 1
So it's -1 ?
what's the degree?
I have no clue
the degree is the highest exponent
take that number, subtract 1 to get the max turning points
So take 14-1 right
So 13 is the answer
yes
Thank you so much!!!!!!
you're welcome

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