Question

The function f(x) is a cubic function and the zeros of f(x) are −1, 2 and 3. Assume the leading coefficient of f(x) is 1. Write the equation of the cubic polynomial in standard form.

Answer 1

The equation of the cubic polynomial f(x) with zeros at -1, 2, and 3, and a leading coefficient of 1 is given in standard form by f(x) = x^3 - 5x^2 + 2x + 6.

Step-by-step explanation:

The question concerns a cubic function with specified zeros and a leading coefficient of 1. Since the zeros of the cubic function f(x) are -1, 2, and 3, we can write the function as the product of its factors corresponding to these zeros:

f(x) = (x + 1)(x - 2)(x - 3)

Expanding this, we get:

f(x) = x(x - 2)(x - 3) + 1(x - 2)(x - 3)

This simplifies to:

f(x) = x^3 - 3x^2 - 2x^2 + 6x + x^2 - 2x - 3x + 6

Combining like terms, we get:

f(x) = x^3 - 5x^2 + 2x + 6

The equation of the cubic polynomial f(x) in standard form is thus:

f(x) = x^3 - 5x^2 + 2x + 6