Polynomials A polynomial is just a sum of power functions where the exponents are all nonnegative whole numbers. Ex: 2 31 412 ( ) 47 3 64 2.315 5 f x x x x x =-+-+ The degree of a polynomial is the biggest exponent. In the example above, deg 412 f = . The number in front of the x with the biggest exponent is the leading coefficient . Above, the leading coefficient is –2.315. These two numbers, along with the variable, make up the polynomial’s leading term . The leading term here is 412 2.315 x-. The leading term eventually dominates the polynomial. If you graph both a polynomial and its leading coefficient in a big enough window, they look identical. The degree and the leading coefficient tell you the end behavior of your graph. As the name implies, the end behavior of the graph is whether the ends of your graph go up or down. If the leading coefficient is positive, the right-hand endpoint points up. If the leading coefficient is negative, then the right-hand endpoint points down. If the degree is even, both
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This note was uploaded on 05/18/2011 for the course MATH 270 taught by Professor Vakarietis during the Summer '08 term at University of Louisiana at Lafayette.