Question

Form a polynomial whose real zeros and degree are given. The zeros are 0, 0, and 0 and the degree is 3. Write a polynomial with integer coefficients and a leading coefficient of 1. Simplify your answer.

Answer 1

The polynomial " x³ "meets all the given criteria, with a leading coefficient of 1 and integer coefficients.

Step-by-step explanation:

To form a polynomial with the given real zeros of 0, 0, and 0 and a degree of 3, with integer coefficients and a leading coefficient of 1, we can use the fact that each zero corresponds to a factor of the polynomial.

For each zero, we can write a factor of (x - zero).

Since all zeros are 0, we have the factors (x - 0), (x - 0), and (x - 0), which simplify to x, x, and x respectively.

Multiplying these factors together, the polynomial is x ³.

This polynomial is already simplified and has integer coefficients.

The leading coefficient is 1 as requested.

The degree of the polynomial is 3, since the highest power of x is 3, which matches with the given degree.