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R_6 - Chapter R Review R.6 1 3 5 Polynomial Division...

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Chapter R 30 Review R.6 Polynomial Division; Synthetic Division 1. quotient, divisor, remainder 2. - 3 2 0 - 5 1 29 3. True 4. True 5. x + 2 4 x 3 - 3 x 2 + x + 1 4 x 3 + 8 x 2 - 11 x 2 + x - 11 x 2 - 22 x 23 x + 1 23 x + 46 - 45 4 x 2 - 11 x + 23 29 Check: ( x + 2)(4 x 2 - 11 x + 23) + ( - 45) = 4 x 3 - 11 x 2 + 23 x + 8 x 2 - 22 x + 46 - 45 = 4 x 3 - 3 x 2 + x + 1 The quotient is 4 x 2 - 11 x + 23; the remainder is –45. 6. x + 2 3 x 3 - x 2 + x - 2 3 x 3 + 6 x 2 - 7 x 2 + x - 7 x 2 - 14 x 15 x - 2 15 x + 30 - 32 3 x 2 - 7 x + 15 29 Check: ( x + 2)(3 x 2 - 7 x + 15) + ( - 32) = 3 x 3 - 7 x 2 + 15 x + 6 x 2 - 14 x + 30 - 32 = 3 x 3 - x 2 + x - 2 The quotient is 3 x 2 - 7 x + 15; the remainder is –32. 7. x 2 4 x 3 - 3 x 2 + x + 1 4 x 3 - 3 x 2 - 3 x 2 x + 1 4 x - 3 29 Check: ( x 2 )(4 x - 3) + ( x + 1) = 4 x 3 - 3 x 2 + x + 1 The quotient is 4 x - 3; the remainder is x + 1 .
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Section R.6 Polynomial Division; Synthetic Division 31 8. x 2 3 x 3 - x 2 + x - 2 3 x 3 - x 2 - x 2 x - 2 3 x - 1 29 Check: ( x 2 )(3 x - 1) + ( x - 2) = 3 x 3 - x 2 + x - 2 The quotient is 3 x - 1 ; the remainder is x - 2. 9. x 2 + 2 5 x 4 - 3 x 2 + x + 1 5 x 4 + 10 x 2 - 13 x 2 + x + 1 - 13 x 2 - 26 x + 27 5 x 2 - 13 29 Check : ( x 2 + 2)(5 x 2 - 13) + ( x + 27) = 5 x 4 - 13 x 2 + 10 x 2 - 26 + x + 27 = 5 x 4 - 3 x 2 + x + 1 The quotient is 5 x 2 - 13 ; the remainder is x + 27. 10. x 2 + 2 5 x 4 - x 2 + x - 2 5 x 4 + 10 x 2 - 11 x 2 + x - 2 - 11 x 2 - 22 x + 20 5 x 2 - 11 29 Check : ( x 2 + 2)(5 x 2 - 11) + ( x + 20) = 5 x 4 - 11 x 2 + 10 x 2 - 22 + x + 20 = 5 x 4 - x 2 + x - 2 The quotient is 5 x 2 - 11 ; the remainder is x + 20. 11. 2 x 3 - 1 4 x 5 - 3 x 2 + x + 1 4 x 5 - 2 x 2 - x 2 + x + 1 2 x 2 29 Check : (2 x 3 - 1)(2 x 2 ) + ( - x 2 + x + 1) = 4 x 5 - 2 x 2 - x 2 + x + 1 = 4 x 5 - 3 x 2 + x + 1 The quotient is 2 x 2 ; the remainder is - x 2 + x + 1.
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