find the number with the highest exponent, that exponent is the degree. for example, 2x to the 3rd power + 6x to the 2nd power the degree is 3
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Not into rational factors.
Usually the sum will have the same degree as the highest degree of the polynomials that are added. However, it is also possible for the highest term to cancel, for example if one polynomial has an x3, and the other a -x3. In this case, the sum will have a lower degree.
put the variable that has the highest degree first.
Not quite. The point at infinity cannot be regarded as a maximum since the value will continue to increase asymptotically. As a result no polynomial of odd degree can have a maximum. Only polynomials of an even degree whose leading coefficient is negative will have a global maximum.
Yes. Here is an example: P1 = 5x4 + 3x3; P2 = -5x4 -2