Question

Suppose that a polynomial function p can be factored into seven factors: (x − 3), (x +1), and 5 factors of (x − 2).What are its zeros with multiplicity, and what is the degree of the polynomial? Explain how you know.

Answer 1

Answer:

From the following equation, the zero 3 has multiplicity with 1 and the zero -1 has multiplicity with 1 and the zero 2 has multiplicity with 5. The degree of the polynomial is 7.

Step-by-step explanation:

The following equation are:

p(x) = (x -3)(x + 1)(x - 2)(x - 2)(x - 2)(x - 2)(x - 2)

Then, the multiplicity of the equation:

p(x) = (x -3)(x + 1)(x - 2)^5

In the following equation, the zero 3 has multiplicity with 1 and the zero -1 has multiplicity with 1, and the zero 2 has multiplicity with 5.

Then the degree of the all polynomials is highest degrees in every term.

So, first we have to expand it:

p(x) = (x -3)(x + 1)(x - 2)^5

p(x) = (x -3)(x + 1)(x - 2)(x - 2)(x - 2)(x - 2)(x - 2)

p(x) = (x^2 + x - 3x - 3)(x^2 - 4x - 4)(x^2 - 4x - 4)(x-2)

p(x) = (x^4 - 6x^3 + 9x^2 + 4x - 12)(x^3 - 6x^2 + 12x - 8)

p(x) = x^7 - 12x^6 + 57x^5 - 130x^4 + 120x^3 + 48x^2 - 176x + 96

so, then the degree of the following equation is 7