Each of Exercises 5–8 shows a complex rational expression and the first step taken to simplify that expression. Indicate for each which method is being used: (a) using division to simplify (Method 1) or (b) multiplying by the LCD (Method 2)
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Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
- For 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_forwardRationalize the numerator of x+10 – 100 Paragraph A.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
- Based on a grade 11 student, answer the following question: Expand the following 2x(3x - y + 1)arrow_forwardExercises 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 -arrow_forwardIn Problems 99–106, analyze each polynomial function farrow_forward
- In Problems 21–32, use Descartes’ Rule of Signs to determine how many positive and how many negative zeros each polynomial functionmay have. Do not attempt to find the zeros.arrow_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_forwardCan you please show me a step by step on how to rationalize this expressionarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage