Question 88430: Hi, I'm trying to understand the topic of Degree of polynomials but I don't
quite get it, and I'm stuck in this problem, how can I determine the degree of
this polynomial?
8x3 + 6x2y + 4xy3 - 2y4
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x^2y^2 + 3x^3 + 4y has degree 4, the same degree as the term x^2y^2.
However, a polynomial in variables x and y, is a polynomial in x with coefficients which are polynomials in y, and also a polynomial in y with coefficients which are polynomials in x.
x^2y^2 + 3x^3 + 4y = (3)x^3 + (y^2)x^2 + (4y) = (x^2)y^2 + (4)y + (3x^3)
This polynomial has degree 3 in x and degree 2 in y.
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Your Problem:
8x^3 + 6x^2y + 4xy^3 - 2y^4 has degree 4
As a polynomial in y it has degree 4
As a polynomial in x it has degree 3
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Cheers,
Stan H.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! Hi, I'm trying to understand the topic of Degree of polynomials but Idon't
quite get it, and I'm stuck in this problem, how can I determine the degree of
this polynomial?
8x3 + 6x2y + 4xy3 - 2y4
The degree of a polynomial is the most number of variables
that are multiplied together in any term of the polynomial
So let's write the eponentials as multiplications of variables:
8x3 + 6x2y + 4xy3 - 2y4 becomes
8xxx + 6xxy + 4xyyy - 2yyyy
The longest strings of multiplied letters are xyyy and yyyy.
Both are strings of 4 multiplied letters, so the degree of the
polynomial is 4.
Edwin
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