Concept explainers
(a)
To calculate: The dividend from the result of the synthetic division process.
(b)
To calculate: The divisor from the result of the synthetic division process.
(c)
To calculate: The quotient from the result of the synthetic division process.
(d)
To calculate: The remainder from the result of the synthetic division process.
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College Algebra Essentials
- 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 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 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_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_forwardIn Problems 21–32, tell the maximum number of real zeros that each polynomial function may have. Then use Descartes’ Rule of Signsto determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zerosarrow_forward
- For Exercises 13–20, factor each expression.arrow_forwardConsider the algebraic expression 3 – 15x*. What is the degree of this polynomial? Identify the constant term. Identify the leading coefficient. Identify the leading term.arrow_forwardFor Exercises 17-18, a. Divide the polynomials. b. Identify the dividend, divisor, quotient, and remainder. 17. (-2x* + x + 4x – 1) ÷ (x² + x - 3) 3x – 2x – 15x + 22x – 8 18. - 3x 2arrow_forward
- In 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_forwardIn Problems 51–68, find the real zeros of f. Use the real zeros to factor f.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
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage