What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial function...
The degree of a polynomial expression tells you the highest power of the variable in the expression. For example, a polynomial expression of degree three would have the highest power of the variable being three.
A polynomial function is a function that can be expressed as a polynomial expression. The degree of the polynomial function tells you the shape and behavior of the graph of the function. The degree also tells you the maximum number of real zeros the function can have.
An example of a polynomial expression of degree three is: f(x) = 2x^3 - 5x^2 + 3x - 1. The related polynomial function is f(x) = 2x^3 - 5x^2 + 3x - 1. The graph of this function would be a curve that can potentially cross the x-axis at most three times. The zeros of the function are the x-values where the graph crosses the x-axis. In this example, the function could have up to three real zeros, which are the x-values that make the function equal to zero.
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The degree of a polynomial expression tells you how many terms the polynomial has. The degree of the polynomial function tells you the shape of the graph and how many times the graph intersects the x-axis.
For example, a polynomial expression of degree three could be something like: f(x) = x^3 - 2x^2 + x + 1. This means the highest power of x in the expression is 3.
The related polynomial function would have a graph that looks like a curved line, and it could cross the x-axis up to three times. The zeros of the function are the values of x where the graph intersects the x-axis. In this case, the function could have up to three real zeros.