Degree of a polynomialThe degree of a polynomial is a very straightforward concept that is really not hard to understand Definition: The degree is the term with the greatest exponent Recall that for y^{2}, y is the base and 2 is the exponent Example #1: 4x^{2} + 6x + 5 This polynomial has three terms. The first one is 4x^{2}, the second is 6x, and the third is 5 The exponent of the first term is 2 The exponent of the second term is 1 because 6x = 6x^{1} The exponent of the third term is 0 because 5 = 5x^{0} What? 5x^{0} = 5? Well, anything with an exponent of 0 is always equal to 1 Thus, 5x^{0} = 5 × x^{0} = 5 × 1 = 5 Since the highest exponent is 2, the degree of 4x^{2} + 6x + 5 is 2 Example #2: 2y^{6} + 1y^{5} + 3y^{4} + 7y^{3} + 9y^{2} + y + 6 This polynomial has seven terms. The first one is 2y^{2}, the second is 1y^{5}, the third is 3y^{4}, the fourth is 7y^{3}, the fifth is 9y^{2}, the sixth is y, and the seventh is 6 The exponent of the first term is 6 The exponent of the second term is 5 The exponent of the third term is 4 The exponent of the fourth term is 3 The exponent of the fifth term is 2 The exponent of the sixth term is 1 because y = y^{1} The exponent of the last term is 0 because 6 = 6x^{0} Since the highest exponent is 6, the degree of 2y^{6} + 1y^{5} + 3y^{4} + 7y^{3} + 9y^{2} + y + 6 is 6 Write a polynomial for the following descriptions 1) A binomial in z with a degree of 10 2) A trinomial in c with a degree of 4 3) A binomial in y with a degree of 1 4) A monomial in b with a degree of 3 Anwers: 1) 2z^{10} − 4 2) c^{4} + c^{2} − 8 3) y + 4 4) b^{3} To find the degree of a polynomial or monomial with more than one variable for the same term, just add the exponents for each variable to get the degree Degree of x^{3}y^{2}. Degree of this monomial = 3 + 2 = 5 




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