Polynomial Degree question

Question

Hi guys I had a quick question? How do you determine the minimum degree of a function. Do you look at the roots or the extrema in the graph? If you do look at the x intercepts couldn't that answer be wrong since you are not accounting for imaginary roots.? Please help I have researched this topic everywhere and have been unable to find a clear and direct answer.THANK YOU!

Answer 1

"Extrema" is the plural; "extremum" is the singular. You have 1 extremum or 2+ extrema.

Answer 2

Looking at the x-intercepts will not help much because of the multiplicity.  By multiplicity, the x-intercepts appear more than once.

 

You can have x-intercepts of  -1 , 2 , and 2.  This does not mean the degree is 3.  Yes, we have 3 x-intercepts, but we only have 2 distinct x-intercepts: -1 and 2.

 

 

Here is an example:

 

x² + 2x + 1 = 0      ------->   (x + 1)(x + 1) = 0

 

has x-intercepts of -1 and -1.   This polynomial has a degree of 2, but there is only 1 distinct x-intercept.   -1

 

 

The best way to determine the degree is to examine the variable's exponents of the quadratic equation's leading term.