CALCULUS APPLIED APPROACH >PRINT UGRADE<
10th Edition
ISBN: 9780357667231
Author: Larson
Publisher: CENGAGE L
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Chapter A4, Problem 70E
To determine
To calculate: The factor the polynomial
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In 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.
In Exercises 35–42, find all real values of x for which fx0. f(x)=4x+6
In 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)
Chapter A4 Solutions
CALCULUS APPLIED APPROACH >PRINT UGRADE<
Ch. A4 - Prob. 1CPCh. A4 - Prob. 2CPCh. A4 - Prob. 3CPCh. A4 - Prob. 4CPCh. A4 - Prob. 1ECh. A4 - Prob. 2ECh. A4 - Prob. 3ECh. A4 - Prob. 4ECh. A4 - Prob. 5ECh. A4 - Prob. 6E
Ch. A4 - Prob. 7ECh. A4 - Prob. 8ECh. A4 - Prob. 9ECh. A4 - Prob. 10ECh. A4 - Prob. 11ECh. A4 - Prob. 12ECh. A4 - Prob. 13ECh. A4 - Prob. 14ECh. A4 - Prob. 15ECh. A4 - Prob. 16ECh. A4 - Factoring Polynomials In Exercises 9-18, write the...Ch. A4 - Prob. 18ECh. A4 - Prob. 19ECh. A4 - Prob. 20ECh. A4 - Prob. 21ECh. A4 - Prob. 22ECh. A4 - Prob. 23ECh. A4 - Prob. 24ECh. A4 - Prob. 25ECh. A4 - Prob. 26ECh. A4 - Prob. 27ECh. A4 - Prob. 28ECh. A4 - Prob. 29ECh. A4 - Prob. 30ECh. A4 - Prob. 31ECh. A4 - Prob. 32ECh. A4 - Prob. 33ECh. A4 - Prob. 34ECh. A4 - Prob. 35ECh. A4 - Prob. 36ECh. A4 - Prob. 37ECh. A4 - Prob. 38ECh. A4 - Prob. 39ECh. A4 - Prob. 40ECh. A4 - Prob. 41ECh. A4 - Prob. 42ECh. A4 - Prob. 43ECh. A4 - Prob. 44ECh. A4 - Prob. 45ECh. A4 - Prob. 46ECh. A4 - Prob. 47ECh. A4 - Prob. 48ECh. A4 - Prob. 49ECh. A4 - Prob. 50ECh. A4 - Prob. 51ECh. A4 - Prob. 52ECh. A4 - Prob. 53ECh. A4 - Prob. 54ECh. A4 - Prob. 55ECh. A4 - Prob. 56ECh. A4 - Prob. 57ECh. A4 - Prob. 58ECh. A4 - Prob. 59ECh. A4 - Prob. 60ECh. A4 - Prob. 61ECh. A4 - Prob. 62ECh. A4 - Prob. 63ECh. A4 - Prob. 64ECh. A4 - Prob. 65ECh. A4 - Prob. 66ECh. A4 - Prob. 67ECh. A4 - Prob. 68ECh. A4 - Prob. 69ECh. A4 - Prob. 70ECh. A4 - Prob. 71ECh. A4 - Prob. 72ECh. A4 - Prob. 73ECh. A4 - Prob. 74ECh. A4 - Prob. 75ECh. A4 - Prob. 76E
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Exercises 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_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_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
- In 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 9–16, a. List all possible rational zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. 9. f(x) = x + x² - 4x – 4 10. f(x) = x - 2x² – 11x + 12 11. f(x) = 2x - 3x? - 11x + 6 12. f(x) = 2r - 5x² + x + 2 13. f(x) = x + 4x² 14. f(x) = 2r + x² - 3x + 1 3x - 6 – 15. f(x) = 2r3 + 6x2 + 5x + 2 16. flx) = x - 4x² + &r – 5arrow_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_forward
- In Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the xaxis, or touches the xaxis and turns around, at each zero. 28. f(x) = -31x + 1/2(x - 4)3 29. f(x)=x3 -2x2 +x30. f(x)=x3 +4x2 +4x31. f(x)=x3 +7x2 -4x-28 32. f(x)=x3 +5x2 -9x-45arrow_forwardFor 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_forwardFor Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11arrow_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_forward(4) Find a polynomial that has 1+i and 1- i as zeros.arrow_forwardFor Exercises 8–10, a. Simplify the expression. Do not rationalize the denominator. b. Find the values of x for which the expression equals zero. c. Find the values of x for which the denominator is zero. 4x(4x – 5) – 2x² (4) 8. -6x(6x + 1) – (–3x²)(6) (6x + 1)2 9. (4x – 5)? - 10. V4 – x² - -() 2)arrow_forward
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