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Unformatted text preview: ssion (2x − 1)3 (x − 2)(3x + 2). The leading term of p will be the term which
has the highest power of x. The way to get this term is to multiply the terms with the highest
power of x from each factor together - in other words, the leading term of p(x) is the product of
the leading terms of the factors of p(x). Hence, the leading term of p is (2x)3 (x)(3x) = 24x5 .
This means the degree of p is 5 and the leading coeﬃcient is 24. As for the constant term,
we can perform a similar trick. The constant term is obtained by multiplying the constant
terms from each of the factors (−1)3 (−2)(2) = 4.
3 Technically, 00 is an indeterminant form, which is a special case of being undeﬁned. The authors realize this is
beyond pedantry, but we wouldn’t mention it if we didn’t feel it was neccessary. 182 Polynomial Functions Our next example shows how polynomials of higher degree arise ‘naturally’4 in even the most basic
Example 3.1.3. A box with no top is to be fashioned from a 10 inch × 12 inch piece of cardboard
by cutting ou...
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