Polynomials in two variables are algebraic

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Unformatted text preview: actions aren’t allowed in polynomials. They just can’t involve the variables. For instance, the following is a polynomial 3 5 x4 - 72 1 x+ x - 5 14 113 12 8 There are lots of radicals and fractions in this algebraic expression, but the denominators of the fractions are only numbers and the radicands of each radical are only a numbers. Each x in the algebraic expression appears in the numerator and the exponent is a positive (or zero) integer. Therefore this is a polynomial. Next, let’s take a quick look at polynomials in two variables. Polynomials in two variables are algebraic expressions consisting of terms in the form ax n y m . The degree of each term in a polynomial in two variables is the sum of the exponents in each term and the degree of the polynomial is the largest such sum. Here are some examples of polynomials in two variables and their degrees. x 2 y - 6 x3 y12 + 10 x 2 - 7 y + 1 degree : 15 6 x 4 + 8 y 4 - xy 2 degree : 4 x 4 y 2 - x 3 y 3 - xy + x 4 degree : 6 6 x - 10 y + 3 x - 11 y degree : 14 14 3 In these kinds of polynomials not every term needs to have both x’s and y’s in them, in...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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