For a polynomial whose zeros and degree are given. Simplify your answer. Zeros: 5, multiplicity 1; −2 multiplicity 2; degree 3. Show all work.

Question

For a polynomial whose zeros and degree are given. Simplify your answer. Zeros: 5, multiplicity 1; −2 multiplicity 2; degree 3. Show all work.

Answer 1

I'm assuming you need to write an equation for the polynomial above.

Since the equation has zeros at 5 and -2 (multiplicity of 2), the associated factors are

(x - 5)(x + 2)(x + 2)

To find the equation, just multiply everything out.

(x - 5)(x² + 2x + 2x +4)

(x - 5)(x² + 4x + 4)

x³ - 5x² + 4x² - 20x + 4x - 20

Then combine like terms for final equation

x³ - x² - 16x - 20