In Exercises 30–33, factor the greatest common factor from each polynomial. 30. 16x3 + 24x² 31. 2x 36x2 32. 21x?y – 14xy² + 7xy 33. 18r'y? – 27x²y
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- In Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.In Exercises 65–74, factor by grouping to obtain the difference of two squares. 6x + 9 – y? 12x + 36 – y? 65. x? 66. x2 67. x + 20xr + 100 68. x? + 16x + 64 – x4 69. 9x2 70. 25x? – 20x + 4 – 81y? 30x + 25 – 36y? 71. x* - x? – 2x – 1 72. x4 -х2 — бх — 9 x? + 4xy – 4y2 x²+ 10xy - 25y2 73. z? 74. z? - rIn 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)
- Exercises 143–145 will help you prepare for the material covered in the next section. In each exercise, factor completely. 143. 2r + 8x? + 8x 144. 5x3 – 40x?y + 35xy2 145. 96?x + 9b²y – 16x – 16y -Exercises 141–143 will help you prepare for the material covered in the next section. In each exercise, factor the polynomial. (You'll soon be learning techniques that will shorten the factoring process.) 141. x? + 14x + 49 142. x? – 8x + 16 143. х2 — 25 (or x? + 0х — 25)In Exercises 34–37, solve each polynomial equation. 34. 3x? = 5x + 2 35. (5x + 4)(x – 1) = 2 36. 15x? – 5x = 0 37. x - 4x2 - x + 4 = 0
- In Exercises 133–136, factor each polynomial completely. Assume that any variable exponents represent whole numbers. 133. y + x + x + y 134. 36x2" – y2n 135. x* 3n 12n 136. 4x2" + 20x"y" + 25y2mExercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2In 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)
- For 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)In 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!In Exercises 35–42, find all real values of x for which fx0. f(x)=4x+6