Question

Write a polynomial in factored form and then convert it to standard form given the zeros are x = 9 (multiplicity 2) and x = 0.

Answer 1

To write the polynomial in factored form, we use the given zeros, x = 9 with a multiplicity of 2 and x = 0. The factored form of the polynomial is (x - 9)(x - 9)(x - 0). To convert it to standard form, expand and simplify the expression: (x - 9)(x - 9)(x - 0) = (x² - 18x + 81)x = x³ - 18x² + 81x.

Step-by-step explanation:

To write the polynomial in factored form, we use the given zeros, x = 9 with a multiplicity of 2 and x = 0. Therefore, the factored form of the polynomial is (x - 9)(x - 9)(x - 0). To convert it to standard form, we need to expand and simplify the expression: (x - 9)(x - 9)(x - 0) = (x - 9)(x - 9)x = (x² - 18x + 81)x = x³ - 18x² + 81x.