College Algebra (10th Edition)
College Algebra (10th Edition)
10th Edition
ISBN: 9780321979476
Author: Michael Sullivan
Publisher: PEARSON
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Roots
The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form o…
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Chapter 5.6, Problem 46DW

f is a polynomial function of degree 4 whose coefficients are real numbers; two of its zeros are − 3 and 4   −   i . Explain why one of the remaining zeros must be a real number. Write down one of the missing zeros.

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Chapter 5 Solutions

College Algebra (10th Edition)

Ch. 5.1 - Prob. 1AYPCh. 5.1 - Prob. 2AYPCh. 5.1 - Prob. 3AYPCh. 5.1 - Prob. 4AYPCh. 5.1 - Prob. 5AYPCh. 5.1 - Prob. 6AYPCh. 5.1 - Prob. 7CVCh. 5.1 - Prob. 8CVCh. 5.1 - Prob. 9CVCh. 5.1 - Prob. 10CV
Ch. 5.1 - Prob. 11CVCh. 5.1 - Prob. 12CVCh. 5.1 - Prob. 13CVCh. 5.1 - Prob. 14CVCh. 5.1 - Prob. 15CVCh. 5.1 - Prob. 16CVCh. 5.1 - Prob. 17SBCh. 5.1 - Prob. 18SBCh. 5.1 - Prob. 19SBCh. 5.1 - Prob. 20SBCh. 5.1 - Prob. 21SBCh. 5.1 - Prob. 22SBCh. 5.1 - Prob. 23SBCh. 5.1 - Prob. 24SBCh. 5.1 - Prob. 25SBCh. 5.1 - Prob. 26SBCh. 5.1 - Prob. 27SBCh. 5.1 - Prob. 28SBCh. 5.1 - Prob. 29SBCh. 5.1 - Prob. 30SBCh. 5.1 - Prob. 31SBCh. 5.1 - Prob. 32SBCh. 5.1 - Prob. 33SBCh. 5.1 - Prob. 34SBCh. 5.1 - Prob. 35SBCh. 5.1 - Prob. 36SBCh. 5.1 - Prob. 37SBCh. 5.1 - Prob. 38SBCh. 5.1 - Prob. 39SBCh. 5.1 - Prob. 40SBCh. 5.1 - Prob. 41SBCh. 5.1 - Prob. 42SBCh. 5.1 - Prob. 43SBCh. 5.1 - Prob. 44SBCh. 5.1 - Prob. 45SBCh. 5.1 - Prob. 46SBCh. 5.1 - Prob. 47SBCh. 5.1 - Prob. 48SBCh. 5.1 - Prob. 49SBCh. 5.1 - Prob. 50SBCh. 5.1 - Prob. 51SBCh. 5.1 - Prob. 52SBCh. 5.1 - Prob. 53SBCh. 5.1 - Prob. 54SBCh. 5.1 - Prob. 55SBCh. 5.1 - Prob. 56SBCh. 5.1 - Prob. 57SBCh. 5.1 - Prob. 58SBCh. 5.1 - Prob. 59SBCh. 5.1 - Prob. 60SBCh. 5.1 - Prob. 61SBCh. 5.1 - Prob. 62SBCh. 5.1 - Prob. 63SBCh. 5.1 - Prob. 64SBCh. 5.1 - Prob. 65SBCh. 5.1 - Prob. 66SBCh. 5.1 - Prob. 67SBCh. 5.1 - Prob. 68SBCh. 5.1 - Prob. 69SBCh. 5.1 - Prob. 70SBCh. 5.1 - Prob. 71SBCh. 5.1 - Prob. 72SBCh. 5.1 - Prob. 73SBCh. 5.1 - Prob. 74SBCh. 5.1 - Prob. 75SBCh. 5.1 - Prob. 76SBCh. 5.1 - Prob. 77SBCh. 5.1 - Prob. 78SBCh. 5.1 - Prob. 79SBCh. 5.1 - Prob. 80SBCh. 5.1 - Prob. 81SBCh. 5.1 - Prob. 82SBCh. 5.1 - Prob. 83SBCh. 5.1 - Prob. 84SBCh. 5.1 - Prob. 85SBCh. 5.1 - Prob. 86SBCh. 5.1 - Prob. 87SBCh. 5.1 - Prob. 88SBCh. 5.1 - Prob. 89SBCh. 5.1 - Prob. 90SBCh. 5.1 - Prob. 91SBCh. 5.1 - Prob. 92SBCh. 5.1 - Prob. 93SBCh. 5.1 - Prob. 94SBCh. 5.1 - Prob. 95SBCh. 5.1 - Prob. 96SBCh. 5.1 - Prob. 97SBCh. 5.1 - Prob. 98SBCh. 5.1 - Prob. 99SBCh. 5.1 - Prob. 100SBCh. 5.1 - Prob. 101SBCh. 5.1 - Prob. 102SBCh. 5.1 - Prob. 103SBCh. 5.1 - Prob. 104SBCh. 5.1 - Prob. 105SBCh. 5.1 - Prob. 106SBCh. 5.1 - Prob. 107MPCh. 5.1 - Prob. 108MPCh. 5.1 - Prob. 109MPCh. 5.1 - Prob. 110MPCh. 5.1 - Prob. 111MPCh. 5.1 - Prob. 112MPCh. 5.1 - Prob. 113MPCh. 5.1 - Prob. 114MPCh. 5.1 - Prob. 115MPCh. 5.1 - Prob. 116MPCh. 5.1 - Prob. 117MPCh. 5.1 - Prob. 118MPCh. 5.1 - Prob. 119MPCh. 5.1 - Prob. 120MPCh. 5.1 - Prob. 121AECh. 5.1 - Prob. 122AECh. 5.1 - Prob. 123AECh. 5.1 - Prob. 124AECh. 5.1 - Prob. 125AECh. 5.1 - Prob. 126DWCh. 5.1 - Prob. 127DWCh. 5.1 - Prob. 128DWCh. 5.1 - Prob. 129DWCh. 5.1 - Prob. 130DWCh. 5.1 - Prob. 131DWCh. 5.1 - Prob. 132DWCh. 5.1 - Prob. 133DWCh. 5.1 - Prob. 134RYKCh. 5.1 - Prob. 135RYKCh. 5.1 - Prob. 136RYKCh. 5.1 - Prob. 137RYKCh. 5.2 - Prob. 1AYPCh. 5.2 - Prob. 2AYPCh. 5.2 - Prob. 3AYPCh. 5.2 - Prob. 4AYPCh. 5.2 - Prob. 5CVCh. 5.2 - Prob. 6CVCh. 5.2 - Prob. 7CVCh. 5.2 - Prob. 8CVCh. 5.2 - Prob. 9CVCh. 5.2 - Prob. 10CVCh. 5.2 - Prob. 11CVCh. 5.2 - Prob. 12CVCh. 5.2 - Prob. 13CVCh. 5.2 - Prob. 14CVCh. 5.2 - Prob. 15CVCh. 5.2 - Prob. 16CVCh. 5.2 - Prob. 17CVCh. 5.2 - Prob. 18CVCh. 5.2 - Prob. 19CVCh. 5.2 - Prob. 20CVCh. 5.2 - Prob. 21CVCh. 5.2 - Prob. 22CVCh. 5.2 - Prob. 23CVCh. 5.2 - Prob. 24CVCh. 5.2 - Prob. 25CVCh. 5.2 - Prob. 26CVCh. 5.2 - Prob. 27CVCh. 5.2 - Prob. 28CVCh. 5.2 - Prob. 29CVCh. 5.2 - Prob. 30CVCh. 5.2 - Prob. 31CVCh. 5.2 - Prob. 32CVCh. 5.2 - Prob. 33CVCh. 5.2 - Prob. 34CVCh. 5.2 - Prob. 35CVCh. 5.2 - Prob. 36CVCh. 5.2 - Prob. 37CVCh. 5.2 - Prob. 38CVCh. 5.2 - Prob. 39CVCh. 5.2 - Prob. 40CVCh. 5.2 - Prob. 41CVCh. 5.2 - Prob. 42CVCh. 5.2 - Prob. 43CVCh. 5.2 - Prob. 44CVCh. 5.2 - Prob. 45CVCh. 5.2 - Prob. 46CVCh. 5.2 - Prob. 47CVCh. 5.2 - Prob. 48CVCh. 5.2 - Prob. 49CVCh. 5.2 - Prob. 50CVCh. 5.2 - Prob. 51CVCh. 5.2 - Prob. 52CVCh. 5.2 - Prob. 53CVCh. 5.2 - Prob. 54CVCh. 5.2 - Prob. 55CVCh. 5.2 - Prob. 56CVCh. 5.2 - Prob. 57AECh. 5.2 - Prob. 58AECh. 5.2 - Prob. 59AECh. 5.2 - Prob. 60AECh. 5.2 - Prob. 61AECh. 5.2 - Prob. 62AECh. 5.2 - Prob. 63DWCh. 5.2 - Prob. 64DWCh. 5.2 - Prob. 65DWCh. 5.2 - Prob. 66DWCh. 5.2 - Prob. 67RYKCh. 5.2 - Prob. 68RYKCh. 5.2 - Prob. 69RYKCh. 5.2 - Prob. 70RYKCh. 5.3 - Prob. 1AYPCh. 5.3 - Prob. 2CVCh. 5.3 - Prob. 3CVCh. 5.3 - Prob. 4CVCh. 5.3 - Prob. 5CVCh. 5.3 - Prob. 6CVCh. 5.3 - Prob. 7SBCh. 5.3 - Prob. 8SBCh. 5.3 - Prob. 9SBCh. 5.3 - Prob. 10SBCh. 5.3 - Prob. 11SBCh. 5.3 - Prob. 12SBCh. 5.3 - Prob. 13SBCh. 5.3 - Prob. 14SBCh. 5.3 - Prob. 15SBCh. 5.3 - Prob. 16SBCh. 5.3 - Prob. 17SBCh. 5.3 - Prob. 18SBCh. 5.3 - Prob. 19SBCh. 5.3 - Prob. 20SBCh. 5.3 - Prob. 21SBCh. 5.3 - Prob. 22SBCh. 5.3 - Prob. 23SBCh. 5.3 - Prob. 24SBCh. 5.3 - Prob. 25SBCh. 5.3 - Prob. 26SBCh. 5.3 - Prob. 27SBCh. 5.3 - Prob. 28SBCh. 5.3 - Prob. 29SBCh. 5.3 - Prob. 30SBCh. 5.3 - Prob. 31SBCh. 5.3 - Prob. 32SBCh. 5.3 - Prob. 33SBCh. 5.3 - Prob. 34SBCh. 5.3 - Prob. 35SBCh. 5.3 - Prob. 36SBCh. 5.3 - Prob. 37SBCh. 5.3 - Prob. 38SBCh. 5.3 - Prob. 39SBCh. 5.3 - Prob. 40SBCh. 5.3 - Prob. 41SBCh. 5.3 - Prob. 42SBCh. 5.3 - Prob. 43SBCh. 5.3 - Prob. 44SBCh. 5.3 - Prob. 45SBCh. 5.3 - Prob. 46SBCh. 5.3 - Prob. 47SBCh. 5.3 - Prob. 48SBCh. 5.3 - Prob. 49SBCh. 5.3 - Prob. 50SBCh. 5.3 - Prob. 51SBCh. 5.3 - Prob. 52SBCh. 5.3 - Prob. 53SBCh. 5.3 - Prob. 54SBCh. 5.3 - Prob. 55AECh. 5.3 - Prob. 56AECh. 5.3 - Prob. 57AECh. 5.3 - Prob. 58AECh. 5.3 - Prob. 59AECh. 5.3 - Prob. 60AECh. 5.3 - Prob. 61AECh. 5.3 - Prob. 62AECh. 5.3 - Prob. 63DWCh. 5.3 - Prob. 64DWCh. 5.3 - Prob. 65DWCh. 5.3 - Prob. 66DWCh. 5.3 - Prob. 67DWCh. 5.3 - Prob. 68DWCh. 5.3 - Prob. 69DWCh. 5.3 - Prob. 70RYKCh. 5.3 - Prob. 71RYKCh. 5.3 - Prob. 72RYKCh. 5.3 - Prob. 73RYKCh. 5.4 - Prob. 1AYPCh. 5.4 - Prob. 2AYPCh. 5.4 - Prob. 3CVCh. 5.4 - Prob. 4CVCh. 5.4 - Prob. 5SBCh. 5.4 - Prob. 6SBCh. 5.4 - Prob. 7SBCh. 5.4 - Prob. 8SBCh. 5.4 - Prob. 9SBCh. 5.4 - Prob. 10SBCh. 5.4 - Prob. 11SBCh. 5.4 - Prob. 12SBCh. 5.4 - Prob. 13SBCh. 5.4 - Prob. 14SBCh. 5.4 - Prob. 15SBCh. 5.4 - Prob. 16SBCh. 5.4 - Prob. 17SBCh. 5.4 - Prob. 18SBCh. 5.4 - Prob. 19SBCh. 5.4 - Prob. 20SBCh. 5.4 - Prob. 21SBCh. 5.4 - Prob. 22SBCh. 5.4 - Prob. 23SBCh. 5.4 - Prob. 24SBCh. 5.4 - Prob. 25SBCh. 5.4 - Prob. 26SBCh. 5.4 - Prob. 27SBCh. 5.4 - Prob. 28SBCh. 5.4 - Prob. 29SBCh. 5.4 - Prob. 30SBCh. 5.4 - Prob. 31SBCh. 5.4 - Prob. 32SBCh. 5.4 - Prob. 33SBCh. 5.4 - Prob. 34SBCh. 5.4 - Prob. 35SBCh. 5.4 - Prob. 36SBCh. 5.4 - Prob. 37SBCh. 5.4 - Prob. 38SBCh. 5.4 - Prob. 39SBCh. 5.4 - Prob. 40SBCh. 5.4 - Prob. 41SBCh. 5.4 - Prob. 42SBCh. 5.4 - Prob. 43SBCh. 5.4 - Prob. 44SBCh. 5.4 - Prob. 45SBCh. 5.4 - Prob. 46SBCh. 5.4 - Prob. 47SBCh. 5.4 - Prob. 48SBCh. 5.4 - Prob. 49MPCh. 5.4 - Prob. 50MPCh. 5.4 - Prob. 51MPCh. 5.4 - Prob. 52MPCh. 5.4 - Prob. 53MPCh. 5.4 - Prob. 54MPCh. 5.4 - Prob. 55MPCh. 5.4 - Prob. 56MPCh. 5.4 - Prob. 57MPCh. 5.4 - Prob. 58MPCh. 5.4 - Prob. 59MPCh. 5.4 - Prob. 60MPCh. 5.4 - Prob. 61MPCh. 5.4 - Prob. 62MPCh. 5.4 - Prob. 63MPCh. 5.4 - Prob. 64MPCh. 5.4 - Prob. 65AECh. 5.4 - Prob. 66AECh. 5.4 - Prob. 67AECh. 5.4 - Prob. 68AECh. 5.4 - Prob. 69AECh. 5.4 - Prob. 70AECh. 5.4 - Prob. 71AECh. 5.4 - Prob. 72AECh. 5.4 - Prob. 73AECh. 5.4 - Prob. 74AECh. 5.4 - Prob. 75AECh. 5.4 - Prob. 76AECh. 5.4 - Prob. 77AECh. 5.4 - Prob. 78AECh. 5.4 - Prob. 79AECh. 5.4 - Prob. 80DWCh. 5.4 - Prob. 81DWCh. 5.4 - Prob. 82DWCh. 5.4 - Prob. 83DWCh. 5.4 - Prob. 84RYKCh. 5.4 - Prob. 85RYKCh. 5.4 - Prob. 86RYKCh. 5.4 - Prob. 87RYKCh. 5.5 - Prob. 1AYPCh. 5.5 - Prob. 2AYPCh. 5.5 - Prob. 3AYPCh. 5.5 - Prob. 4AYPCh. 5.5 - Prob. 5CVCh. 5.5 - Prob. 6CVCh. 5.5 - Prob. 7CVCh. 5.5 - Prob. 8CVCh. 5.5 - Prob. 9CVCh. 5.5 - Prob. 10CVCh. 5.5 - Prob. 11SBCh. 5.5 - Prob. 12SBCh. 5.5 - Prob. 13SBCh. 5.5 - Prob. 14SBCh. 5.5 - Prob. 15SBCh. 5.5 - Prob. 16SBCh. 5.5 - Prob. 17SBCh. 5.5 - Prob. 18SBCh. 5.5 - Prob. 19SBCh. 5.5 - Prob. 20SBCh. 5.5 - Prob. 21SBCh. 5.5 - Prob. 22SBCh. 5.5 - Prob. 23SBCh. 5.5 - Prob. 24SBCh. 5.5 - Prob. 25SBCh. 5.5 - Prob. 26SBCh. 5.5 - Prob. 27SBCh. 5.5 - Prob. 28SBCh. 5.5 - Prob. 29SBCh. 5.5 - Prob. 30SBCh. 5.5 - Prob. 31SBCh. 5.5 - Prob. 32SBCh. 5.5 - Prob. 33SBCh. 5.5 - Prob. 34SBCh. 5.5 - Prob. 35SBCh. 5.5 - Prob. 36SBCh. 5.5 - Prob. 37SBCh. 5.5 - Prob. 38SBCh. 5.5 - Prob. 39SBCh. 5.5 - Prob. 40SBCh. 5.5 - Prob. 41SBCh. 5.5 - Prob. 42SBCh. 5.5 - Prob. 43SBCh. 5.5 - Prob. 44SBCh. 5.5 - Prob. 45SBCh. 5.5 - Prob. 46SBCh. 5.5 - Prob. 47SBCh. 5.5 - Prob. 48SBCh. 5.5 - Prob. 49SBCh. 5.5 - Prob. 50SBCh. 5.5 - Prob. 51SBCh. 5.5 - Prob. 52SBCh. 5.5 - Prob. 53SBCh. 5.5 - Prob. 54SBCh. 5.5 - Prob. 55SBCh. 5.5 - Prob. 56SBCh. 5.5 - Prob. 57SBCh. 5.5 - Prob. 58SBCh. 5.5 - Prob. 59SBCh. 5.5 - Prob. 60SBCh. 5.5 - Prob. 61SBCh. 5.5 - Prob. 62SBCh. 5.5 - Prob. 63SBCh. 5.5 - Prob. 64SBCh. 5.5 - Prob. 65SBCh. 5.5 - Prob. 66SBCh. 5.5 - Prob. 67SBCh. 5.5 - Prob. 68SBCh. 5.5 - Prob. 69SBCh. 5.5 - Prob. 70SBCh. 5.5 - Prob. 71SBCh. 5.5 - Prob. 72SBCh. 5.5 - Prob. 73SBCh. 5.5 - Prob. 74SBCh. 5.5 - Prob. 75SBCh. 5.5 - Prob. 76SBCh. 5.5 - Prob. 77SBCh. 5.5 - Prob. 78SBCh. 5.5 - Prob. 79SBCh. 5.5 - Prob. 80SBCh. 5.5 - Prob. 81SBCh. 5.5 - Prob. 82SBCh. 5.5 - Prob. 83SBCh. 5.5 - Prob. 84SBCh. 5.5 - Prob. 85SBCh. 5.5 - Prob. 86SBCh. 5.5 - Prob. 87SBCh. 5.5 - Prob. 88SBCh. 5.5 - Prob. 89SBCh. 5.5 - Prob. 90SBCh. 5.5 - Prob. 91SBCh. 5.5 - Prob. 92SBCh. 5.5 - Prob. 93MPCh. 5.5 - Prob. 94MPCh. 5.5 - Prob. 95MPCh. 5.5 - Prob. 96MPCh. 5.5 - Prob. 97MPCh. 5.5 - Prob. 98MPCh. 5.5 - Prob. 99MPCh. 5.5 - Prob. 100MPCh. 5.5 - Prob. 101MPCh. 5.5 - Prob. 102MPCh. 5.5 - Prob. 103MPCh. 5.5 - Prob. 104MPCh. 5.5 - Prob. 105MPCh. 5.5 - Prob. 106MPCh. 5.5 - Prob. 107AECh. 5.5 - Prob. 108AECh. 5.5 - Prob. 109AECh. 5.5 - Prob. 110AECh. 5.5 - Prob. 111AECh. 5.5 - Prob. 112AECh. 5.5 - Prob. 113AECh. 5.5 - Prob. 114AECh. 5.5 - Prob. 115AECh. 5.5 - Prob. 116AECh. 5.5 - Prob. 117AECh. 5.5 - Prob. 118AECh. 5.5 - Prob. 119AECh. 5.5 - Prob. 120DWCh. 5.5 - Prob. 121DWCh. 5.5 - Prob. 122DWCh. 5.5 - Prob. 123DWCh. 5.5 - Prob. 124RYKCh. 5.5 - Prob. 125RYKCh. 5.5 - Prob. 126RYKCh. 5.5 - Prob. 127RYKCh. 5.6 - Prob. 1AYPCh. 5.6 - Prob. 2AYPCh. 5.6 - Prob. 3CVCh. 5.6 - Prob. 4CVCh. 5.6 - Prob. 5CVCh. 5.6 - Prob. 6CVCh. 5.6 - Prob. 7SBCh. 5.6 - Prob. 8SBCh. 5.6 - Prob. 9SBCh. 5.6 - Prob. 10SBCh. 5.6 - Prob. 11SBCh. 5.6 - Prob. 12SBCh. 5.6 - Prob. 13SBCh. 5.6 - Prob. 14SBCh. 5.6 - Prob. 15SBCh. 5.6 - Prob. 16SBCh. 5.6 - Prob. 17SBCh. 5.6 - Prob. 18SBCh. 5.6 - Prob. 19SBCh. 5.6 - Prob. 20SBCh. 5.6 - Prob. 21SBCh. 5.6 - Prob. 22SBCh. 5.6 - Prob. 23SBCh. 5.6 - Prob. 24SBCh. 5.6 - Prob. 25SBCh. 5.6 - Prob. 26SBCh. 5.6 - Prob. 27SBCh. 5.6 - Prob. 28SBCh. 5.6 - Prob. 29SBCh. 5.6 - Prob. 30SBCh. 5.6 - Prob. 31SBCh. 5.6 - Prob. 32SBCh. 5.6 - Prob. 33SBCh. 5.6 - Prob. 34SBCh. 5.6 - Prob. 35SBCh. 5.6 - Prob. 36SBCh. 5.6 - Prob. 37SBCh. 5.6 - Prob. 38SBCh. 5.6 - Prob. 39SBCh. 5.6 - Prob. 40SBCh. 5.6 - Prob. 41MPCh. 5.6 - Prob. 42MPCh. 5.6 - Prob. 43MPCh. 5.6 - Prob. 44DWCh. 5.6 - Prob. 45DWCh. 5.6 - f is a polynomial function of degree 4 whose...Ch. 5.6 - Prob. 47DWCh. 5.6 - Prob. 48DWCh. 5.6 - Prob. 49RYKCh. 5.6 - Prob. 50RYKCh. 5.6 - Prob. 51RYKCh. 5.6 - Prob. 52RYKCh. 5.R - Prob. 1RECh. 5.R - Prob. 2RECh. 5.R - Prob. 3RECh. 5.R - Prob. 4RECh. 5.R - Prob. 5RECh. 5.R - Prob. 6RECh. 5.R - Prob. 7RECh. 5.R - Prob. 8RECh. 5.R - Prob. 9RECh. 5.R - Prob. 10RECh. 5.R - Prob. 11RECh. 5.R - Prob. 12RECh. 5.R - Prob. 13RECh. 5.R - Prob. 14RECh. 5.R - Prob. 15RECh. 5.R - Prob. 16RECh. 5.R - Prob. 17RECh. 5.R - Prob. 18RECh. 5.R - Prob. 19RECh. 5.R - Prob. 20RECh. 5.R - Prob. 21RECh. 5.R - Prob. 22RECh. 5.R - Prob. 23RECh. 5.R - Prob. 24RECh. 5.R - Prob. 25RECh. 5.R - Prob. 26RECh. 5.R - Prob. 27RECh. 5.R - Prob. 28RECh. 5.R - Prob. 29RECh. 5.R - Prob. 30RECh. 5.R - Prob. 31RECh. 5.R - Prob. 32RECh. 5.R - Prob. 33RECh. 5.R - Prob. 34RECh. 5.R - Prob. 35RECh. 5.R - Prob. 36RECh. 5.R - Prob. 37RECh. 5.R - Prob. 38RECh. 5.R - Prob. 39RECh. 5.R - Prob. 40RECh. 5.R - Prob. 41RECh. 5.R - Prob. 42RECh. 5.R - Prob. 43RECh. 5.R - Prob. 44RECh. 5.R - Prob. 45RECh. 5.R - Prob. 46RECh. 5.R - Prob. 47RECh. 5.R - Prob. 48RE
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