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Stitz-Zeager_College_Algebra_e-book

# Applying the upper bound portion to f x gives the

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Unformatted text preview: he indicated division. Write the polynomial in the form p(x) = d(x)q (x) + r(x). (a) (5x4 − 3x3 + 2x2 − 1) ÷ (x2 + 4) (c) (9x3 + 5) ÷ (2x − 3) (b) (−x5 + 7x3 − x) ÷ (x3 − x2 + 1) (d) (4x2 − x − 23) ÷ (x2 − 1) 2. Use synthetic division and the Remainder Theorem to test whether or not the given number is a zero of the polynomial p(x) = 15x5 − 121x4 + 17x3 − 73x2 + 2x + 48. 2 3 (a) c = −1 (d) c = (b) c = 8 (e) c = 0 (c) c = 1 2 3 (f) c = − 5 3. For each polynomial given below, you are given one of its zeros. Use the techniques in this section to ﬁnd the rest of the real zeros and factor the polynomial. (a) x3 − 6x2 + 11x − 6, c = 1 (b) x3 − 24x2 + 192x − 512, c = 8 (c) 4x4 − 28x3 + 61x2 − 42x + 9, c = (d) 3x3 + 4x2 − x − 2, c = (e) x4 − x2 , c = 0 (f) x2 − 2x − 2, c = 1 − 1 2 2 3 √ 3 3 (g) 125x5 − 275x4 − 2265x3 − 3213x2 − 1728x − 324, c = − 5 4. Create a polynomial p with the following attributes. • As x → −∞, p(x) → ∞. • The point (−2, 0) yields a local maximum. • The degree of p is 5. • The point (3, 0) is one of the x-intercepts of the graph...
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