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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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