Question

Explain how the factored form of a polynomial helps us in graphing it. In your explanation be sure to address the idea of multiplicity of a factor and how that impacts the graph. Please include an example in your explanation..

Answer 1

We will explain how the factored form of a polynomial helps us in graphing it.

The factored form write the equation using the zeros of the polynomial

the zeros are the point of intersection between the graph of the polynomial and the x-axis

The number of zeros defines the type of the polynomial

For example: if the number of zeros = 1, the function will be linear

if the number of zeros = 2, the function will be a parabola (quadratic function)

Also, we can find the interval of increase and decrease beside the concavity of the graph.