Question

Write a polynomial function in standard form with real coefficients, leading coefficient 1, degree 3, and zeros: -1, 2 (multiplicity 2).

A) Construct the polynomial function.
B) Identify the degree and leading coefficient.
C) Determine the real coefficients.
D) Confirm the correctness of the standard form.

Answer 1

To write a polynomial function in standard form with real coefficients, we use the factored form and plug in the given information to get f(x) = x^3 - 3x^2 - 6x + 4.

Step-by-step explanation:

To write a polynomial function in standard form with real coefficients, leading coefficient 1, degree 3, and zeros -1 and 2 (multiplicity 2), we can use the factored form of a polynomial. The factored form is given by f(x) = a(x - r1)(x - r2)(x - r3), where 'a' is the leading coefficient and 'r1, r2, r3' are the zeros. Plugging in the given information, we have f(x) = (x + 1)(x - 2)(x - 2).

Expanding this expression, we get f(x) = (x + 1)(x^2 - 4x + 4). Multiplying these binomials, we have f(x) = x^3 - 3x^2 - 6x + 4.