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**Unformatted text preview: **5 3. h(x) = 2. g (x) = 12x + x3 4. p(x) = (2x − 1)3 (x − 2)(3x + 2) Solution.
1. There are no surprises with f (x) = 4x5 − 3x2 + 2x − 5. It is written in the form of Deﬁnition
3.2, and we see the degree is 5, the leading term is 4x5 , the leading coeﬃcient is 4 and the
constant term is −5.
2. The form given in Deﬁnition 3.2 has the highest power of x ﬁrst. To that end, we re-write
g (x) = 12x + x3 = x3 + 12x, and see the degree of g is 3, the leading term is x3 , the leading
coeﬃcient is 1 and the constant term is 0.
3. We need to rewrite the formula for h so that it resembles the form given in Deﬁnition 3.2:
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h(x) = 4−x = 4 − x = − 1 x + 4 . We see the degree of h is 1, the leading term is − 5 x, the
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leading coeﬃcient is − 1 and the constant term is 5 .
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4. It may seem that we have some work ahead of us to get p in the form of Deﬁnition 3.2.
However, it is possible to glean the information requested about p without multiplying out
the entire expre...

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