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Unformatted text preview: parate off constant functions from the other polynomials in Definition 3.2. Why not just lump them all together and, instead of forcing n to be a natural number, n = 1, 2, . . ., let n be a whole number, n = 0, 1, 2, . . .. We could unify all the cases, since, after all, isn’t a0 x0 = a0 ? The answer is ‘yes, as long as x = 0.’ The function f (x) = 3 and g (x) = 3x0 are different, because their domains are different. The number f (0) = 3 is defined, whereas g (0) = 3(0)0 is not.3 Indeed, much of the theory we will develop in this chapter doesn’t include the constant functions, so we might as well treat them as outsiders from the start. One good thing that comes from Definition 3.2 is that we can now think of linear functions as degree 1 (or ‘first degree’) polynomial functions and quadratic functions as degree 2 (or ‘second degree’) polynomial functions. Example 3.1.2. Find the degree, leading term, leading coefficient and constant term of the following polynomial functions. 4−x 5 1. f (x) = 4x5 − 3x2 + 2x ...
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