More Polynomial Investigation

The roots of a polynomial function, p(x), are the solutions of the equation p(x)=0. Another name for the roots of a function is zeros of a function because at each root, the value of the function is zero. The real roots (or zeros) of a function have the same value as the x-values of the x-intercepts of its graph because the -intercepts are the points where the y-value of the function is zero.

Sometimes roots can be found by factoring and solving for p(x)=0.

Can a polynomial of n degree have fewer than n number of roots?

You can use a number line to represent the -values for which a polynomial graph is above or below the x-axis. The bold parts of each number line below show where the output values of a polynomial function are positive. That is, where the graph is above the x-axis. The open circles show locations of the -intercepts or roots of the function. Where there is no shading, the value of the function is negative. Write a possible equation.

You can use a number line to represent the -values for which a polynomial graph is above or below the x-axis. The bold parts of each number line below show where the output values of a polynomial function are positive. That is, where the graph is above the x-axis. The open circles show locations of the -intercepts or roots of the function. Where there is no shading, the value of the function is negative. Write a possible equation. 

When the y-values of a graph get very large as the x-values get large, the graph has positive orientation. When the y-values of a graph get very small as the x-values get large, the graph has negative orientation.