Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. -2, 1, 3

Answer 1

Step-by-step explanation:

A polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 1, 3 is (x- -2)(x-1)(x-3) = x^3 - 6x^2 + 11x - 6

Answer 2

To find a polynomial function with rational coefficients, a leading coefficient of 1, and the given zeros (-2, 1, 3), we can use the factored form of a polynomial with roots a, b, and c.

Step-by-step explanation:

To find a polynomial function with rational coefficients, a leading coefficient of 1, and the given zeros (-2, 1, 3), we can use the fact that the polynomial with roots x = a, x = b, and x = c can be written in factored form as (x - a)(x - b)(x - c).

Using this formula, we have (x + 2)(x - 1)(x - 3) as the factored form of our polynomial.

Expanding this, we get (x + 2)(x^2 - 4x + 3) which simplifies to x^3 - 4x^2 + 3x + 6. Therefore, f(x) = x^3 - 4x^2 + 3x + 6 is the polynomial function of least degree in standard form.