Answer :
Final answer:
A polynomial of the right degree, specifically is (x - (-3))(x - 3)(x - 4)(x - 5), which is a fourth-degree polynomial.
Explanation:
The given zeros and degree can be used to construct the polynomial. From these zeros, we form factors of the form '(x - r)' and then multiply these factors together. To form a polynomial given the zeros and the degree, one should understand that the zeros of a polynomial are the solutions to the equation where the polynomial is equal to zero.
In this particular case, the zeros are -3,3,4,5 and the polynomial's degree is 4. We can form a polynomial by multiplying factors based on these zeros. Each zero 'r' contributes to a factor of '(x-r)'. Therefore, the polynomial is (x - (-3))(x - 3)(x - 4)(x - 5).
Also, considering that the degree of the polynomial is 4 and since each of these factors is a first-degree polynomial, this polynomial will indeed be a fourth-degree polynomial once simplified, which matches with the degree given in the problem.
Learn more about Polynomials here:
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