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Answer :
To form a polynomial with zeros -4, -3, 1, and 4 of degree 4, we multiply the factors (x + 4), (x + 3), (x - 1), and (x - 4) to get the expanded polynomial x^4 + 2x^3 - 19x^2 + 48x + 48. Therefore, the correct option is A.
To form a polynomial with given zeros and a specific degree, we can start by forming factors from each zero. The zeros given are -4, -3, 1, and 4, and the polynomial is of degree 4 with a leading coefficient of 1. To create the polynomial, we use the fact that if 'a' is a zero of the polynomial, then '(x - a)' is a factor of the polynomial.
The factors corresponding to the given zeros are:
Multiplying these factors together gives us the polynomial:
(x + 4) * (x + 3) * (x - 1) * (x - 4)
After expanding and simplifying, we obtain the polynomial:
x4 + 2x3 - 19x2 + 48x + 48
Hence, the correct polynomial with the given zeros and degree is x4 + 2x3 - 19x2 + 48x + 48, which corresponds to option A.
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