High School

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Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

Zeros: -4, -3, 1, 4; Degree: 4

Select one:

A. \(x^4 + 2x^3 - 19x^2 + 48x + 48\)

B. \(x^4 + 2x^3 - 19x^2 - 32x + 48\)

C. \(x^4 + 16x^2 + 48\)

D. \(x^4 - 2x^3 - 19x^2 + 32x + 48\)

Answer :

To form the polynomial with the zeros -4, -3, 1, and 4, we create factors for each zero and multiply them together. After expanding these factors, we find that option A, (x4 + 2x3 - 19x2 + 48x + 48), is the correct polynomial.Thus, the correct option is A.

To form a polynomial with given zeros -4, -3, 1, and 4, and a degree of 4 with a leading coefficient of 1, we should use the fact that if 'a' is a zero of a polynomial then (x - a) is a factor of that polynomial. Therefore, the polynomial with the given zeros is the product of the factors (x + 4), (x + 3), (x - 1), and (x - 4).

Expanding these factors, we get:

(x + 4)(x + 3)(x - 1)(x - 4)

Simplifying step by step, we obtain the following:

(x2 + 7x + 12)(x2 - 5x - 4)

Continuing the expansion:

(x4 + 2x3 - 19x2 + 48x + 48)

Thus, the correct option is A. x4 + 2x3 - 19x2 + 48x + 48.

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