Question

write a polynomial equation with integer coefficients that has the given roots.

\\(x = 0, x = 4, x = -2\\)

Explanation:

Identify the factors from the given roots

Using the Zero Product Property knowledge point

$$
LATEXBLOCK0
$$

Set up the polynomial equation

Using the Zero Product Property knowledge point

$$ x(x - 4)(x + 2) = 0 $$

Multiply the binomial factors

Using the Polynomial Multiplication knowledge point

$$ (x - 4)(x + 2) = x^2 + 2x - 4x - 8 = x^2 - 2x - 8 $$

Distribute the remaining variable

Using the Polynomial Multiplication knowledge point

$$ x(x^2 - 2x - 8) = x^3 - 2x^2 - 8x = 0 $$

Answer:

\(x^3 - 2x^2 - 8x = 0\)