Concept explainers
For Exercises 31–34, consider the division of two polynomials: f(x) + (x– c). The result of the synthetic division process is shown here. Write the polynomials representing the
a. Dividend.
b. Divisor.
c. Quotient.
d. Remainder.
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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 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_forwardIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. 2. f(x)=7x2 +9x4 3. g(x) = 7x5 - px3 + 1/5x 5. h(x) = 7x3 +2x2 + 1/x 7. f(x)=x1/2 -3x2 +5arrow_forward
- Consider 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 13–20, factor each expression.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
- 2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity. %3D |arrow_forwardIn Problems 51–68, find the real zeros of f. Use the real zeros to factor f.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
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage