Concept explainers
Divide and if there is a remainder, express it in two ways. Use synthetic division in Exercises 28–30. [5.3b, c]
Janine found that the sum of two rational expressions was
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- 5. Consider the following division: (2,3 – 4x² + x – 2)÷ (x – 2) - 5a Fill in the gaps to complete the long division process below. + Ox + х — 2 | 2х3 - 4x² + lxarrow_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_forwardSolve the following polynomial equation 2.10)arrow_forward
- b) Rationalize the numerator of 1 1 3x √3(x+h) h Simplify your answer to the form as h 0 1 where A " = as longarrow_forwardFor Exercises 23–28, write the answer as a single term and simplify. It is not necessary to rationalize the denominator. 2Vx + 4 2rV16 – * + Vx + 4 V16 – x 23. 24. (Vx + 4) (V16 – x) 25. (х — 4)/3 26. (х + 5)/4 + + 3(x 4)2/3 4(x + 5)3/4 2x -1/2[ (x + 1)(2) – 2x(1) 3x -2/3[ (x + 1) • 3 – 3x(2x) 27. 28. \x + 1. (x + 1)? x² + (x? + 1)?arrow_forwardAbstract Algebra:arrow_forward
- 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)arrow_forwardb) Rationalize the numerator of 1 1 √Tx √7(x + h) h Simplify your answer to the form A = = A " wherearrow_forward67. Calculate the discriminant associated with the equation 6x2+5x+1=0.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning