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For Exercises 43–46, use the remainder theorem to evaluate the polynomial for the given values of x. (See Example 6)
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COLLEGE ALGEBRA CUSTOM -ALEKS ACCESS
- For Exercises 69–84, find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) 69. f(x) = 8x – 42x + 33x + 28 (Hint: See Exercise 61.) 6x – x? (Hint: See Exercise 62.) 70. f(x) - 57x + 70 72. f(x) = 3x – 16x + 5x + 90x (Hint: See Exercise 64.) 2x + 11x - 63x? - 50x + 40 71. f(x) = (Hint: See Exercise 63.) - 138x + 36arrow_forwardIn Exercises 9–12, find a first- degree polynomial function P1 whose value and slope agree with the value and slope of f at x = c. Use a graphing utility to graph f and P1.arrow_forwardIn Exercises 26–31, find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. 26. n= 3; 4 and 2i are zeros; f(-1) = -50 31. n= 4; -2, 5, and 3 + 2i are zeros; f(1) = -96arrow_forward
- In Exercises 35–42, find all real values of x for which fx0. f(x)=4x+6arrow_forwardIn Exercises 12–20, find all zeros of each polynomial function. Then graph the function. 12. f(x) = (x – 2)°(x + 1)³ 13. f(x) = -(x – 2)(x + 1)? 14. f(x) = x - xr? – 4x + 4 15. f(x) = x* - 5x² + 4 16. f(x) = -(x + 1)° 17. f(x) = -6x³ + 7x? - 1 18. f(x) = 2r³ – 2x 19. f(x) = x - 2x² + 26x 20. f(x) = -x + 5x² – 5x – 3 %3D %3D %3! %3D %3!arrow_forwardExercises 47 D–520: The graph of either a cubic, quartic, or quintic polynomial f(x) with integer zeros is shown. Write the complete factored form of f(x). (Hint: In Exercises 51 O and 52 O the leading coefficient is not +1.)arrow_forward
- In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). 18x4 + 9x3 + 3x2 /3x2+1 In Exercises 17–25, divide using synthetic division. 17. (2x2 +x-10)/(x-2) 25. (x2 -5x-5x3 +x4)/(5+x)arrow_forwardIn Exercises 130–133, use a graphing utility to graph the functions y, and y2. Select a viewing rectangle that is large enough to show the end behavior of y2. What can you conclude? Verify your conclusions using polynomial multiplication. 130. yı = (x - 2)² y2 = x2 – 4x + 4 131. yı = (x – 4)(x² y2 = x - 7x2 + 14x – 8 132. yı = (x – 1)(x + x + 1) y2 = x – 1 133. yı = (x + 1.5)(x – 1.5) y2 = x? – 2.25 3x + 2)arrow_forwardIn Problems 51–68, find the real zeros of f. Use the real zeros to factor f.arrow_forward
- In Problems 17–28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tellwhy not. Write each polynomial in standard form. Then identify the leading term and the constant termarrow_forwardIn Exercises 83–86, determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false. If the graph of a polynomial function has three x-intercepts,then it must have at least two points at which its tangent line ishorizontal.arrow_forwardIn Problems 33–44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rationalzeros of each polynomial function. Do not attempt to find the zeros.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage