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Stitz-Zeager_College_Algebra_e-book

# Since this doesnt factor nicely we use the quadratic

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Unformatted text preview: 4) Degree 5 Leading term 5t5 Leading coeﬃcient 5 Constant term 0 As t → −∞, p(t) → −∞ As t → ∞, p(t) → ∞ (e) P (x) = (x − 1)(x − 2)(x − 3)(x − 4) Degree 4 Leading term x4 Leading coeﬃcient 1 Constant term 24 As x → −∞, P (x) → ∞ As x → ∞, P (x) → ∞ (c) Z (b) = 42b − b3 Degree 3 Leading term −b3 Leading coeﬃcient −1 Constant term 0 As b → −∞, Z (b) → ∞ As b → ∞, Z (b) → −∞ (f) q (r) = 1 − 16r4 Degree 4 Leading term −16r4 Leading coeﬃcient −16 Constant term 1 As r → −∞, q (r) → −∞ As r → ∞, q (r) → −∞ 2. (a) a(x) = x(x + 2)2 x = 0 multiplicity 1 x = −2 multiplicity 2 (b) F (x) = x3 (x + 2)2 x = 0 multiplicity 3 x = −2 multiplicity 2 y −2 −1 y x −2 −1 x 194 Polynomial Functions (c) P (x) = (x − 1)(x − 2)(x − 3)(x − 4) x = 1 multiplicity 1 x = 2 multiplicity 1 x = 3 multiplicity 1 x = 4 multiplicity 1 (e) Q(x) = (x + 5)2 (x − 3)4 x = −5 multiplicity 2 x = 3 multiplicity 4 y y −5 −4 −3 −2 −1 1 2 3...
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