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The degree of a polynomial is determined by the highest degree of the terms within it, and the degree of the terms is determined by the power of the variable and the amount of variables in it.
For example, the term 3x has a degree of one, as does 5y. However when there is more than one variable you add the degrees together, so 4xy has a degree of 2, not 1. Any single variable to the 2nd power e.g. 8x2 also has a degree of 2.
So a polynomial of one degree is a polynomial where each of its terms only have one variable to the first power so 5+x is to one degree, as is 1+2x+3y+4z despite having more than one variable in the expression.
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Can all cubic polynomials be factored into polynomials of degree 1 or 2?
Not into rational factors.
How is the degree of of the sum related to the degree of the original polynomials?
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.
All polynomials have at least one maximum?
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.
What is the correct order in which polynomials be always written?
put the variable that has the highest degree first.
How do you state the degree of a polynomials?
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
