Final answer:
To create a third degree polynomial with a leading coefficient of 1, use its zeros to form factors and multiply them. For example, with zeros of 2, -3, and 4, the polynomial is (x - 2)(x + 3)(x - 4) which expands to x^3 - 3x^2 - 10x + 24.
Step-by-step explanation:
The question pertains to the creation of a third degree polynomial equation with a leading coefficient of 1 and given zeros. To construct such a polynomial, we take the zeros of the polynomial and use them to form factors, which when multiplied together will give us the desired polynomial. For example, if the given zeros are 2, -3, and 4, then we would have three factors: (x - 2), (x + 3), and (x - 4). The resulting third degree polynomial with these zeros and a leading coefficient of 1 is (x - 2)(x + 3)(x - 4). When multiplied out, this would yield x^3 - 3x^2 - 10x + 24, which is the required polynomial.
In general, a third degree polynomial with leading coefficient 1 and zeros a, b, and c can be written as (x - a)(x - b)(x - c). This method utilizes the fact that the zeros of a polynomial are the values for which the polynomial equals zero, and thus they correspond to the roots of the equation formed by setting the polynomial equal to zero.