Question

form a polynomial whose real zeros and degree are given.

zeros: -4, 0, 3; degree: 3

a polynomial with integer coefficients and a leading coefficient of 1 is f(x) = (simplify your answer.)

Explanation:

Write the factored form of the polynomial

$$ f(x) = a(x - z_1)(x - z_2)(x - z_3) $$

$$ f(x) = 1 \cdot (x - (-4))(x - 0)(x - 3) = x(x + 4)(x - 3) $$

Expand the factored expression

$$ f(x) = x(x^2 + 4x - 3x - 12) $$

$$ f(x) = x(x^2 + x - 12) $$

Distribute the variable x

$$ f(x) = x^3 + x^2 - 12x $$

Answer:

A polynomial with integer coefficients and a leading coefficient of 1 is \(f(x) =\) <blank>\(x^3 + x^2 - 12x\)</blank>