A polynomial that has zeros at 1, 2, and 3 with multiplicities of 1, 2, and 3 respectively.
-Represent a function that satisfies the given conditions by an equation. Leave in factored form.
(x-1)(x-2)^2(x-3)^3
To represent a polynomial function that satisfies the given conditions, we start by writing the equation in factored form. Since the polynomial has zeros at 1, 2, and 3, we can write the equation as follows:
f(x) = (x - 1)(x - 2)^2(x - 3)^3
In this equation, (x - 1) represents a zero with a multiplicity of 1, (x - 2)^2 represents a zero with a multiplicity of 2, and (x - 3)^3 represents a zero with a multiplicity of 3.