X2 x 1 x4 x 2 x 1 x2 x 3 2x 2 x 3 x 2

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Unformatted text preview: 1 2x + 2 +1 x4 + x3 + x2 Check : (x 2 + x + 1)( x 2 - x -1) + (2x + 2) = x 4 - x 3 - x 2 + x 3 - x 2 - x + x 2 - x -1+ 2x + 2 = x4 - x2 +1 The quotient is x 2 - x - 1; the remainder is 2x + 2. 18. x2 - x +1 x4 4 3 ) x 2 + x -1 - x2 2 +1 x - x +x x 3 - 2x 2 x3 - x2 + x - x2 - x + 1 -x 2 + x -1 - 2x + 2 Check: (x 2 - x + 1)(x 2 + x - 1) + (- 2x + 2) = x 4 + x 3 - x 2 - x 3 - x 2 + x + x 2 + x - 1- 2x + 2 = x4 - x 2 + 1 The quotient is x 2 + x - 1; the remainder is - 2x + 2 . 33 Chapter R 19. x-a x Review x 2 + ax + a 2 3 ) Check : -a 3 (x - a)(x 2 + ax + a 2 ) + 0 = x 3 + ax 2 + a 2 x - ax 2 - a 2 x - a 3 = x 3 - a3 x 3 - ax 2 ax 2 ax 2 - a 2 x a x-a 2 3 The quotient is x 2 + ax + a 2 ; the remainder is 0. a2 x - a3 0 20. x 4 + ax 3 + a 2 x 2 + a 3 x + a 4 - a5 ax 4 ax 4 - a 2 x 3 a2 x 3 a2 x 3 - a3 x 2 a3 x 2 a3 x 2 - a4 x a4 x - a5 a4 x - a5 0 21. 2) 1 - 1 2 1 1 -1)1 2 4 2 8 4 12 Quotient: x 2 + x + 4 Remainder: 12 Quotient: x 2 + x - 4 Remainder: 5 Quotient: 3x 2 + 11x + 32 Remainder: 99 = x 5 - a5 The quotient is x 4 + ax 3 + a2 x 2 + a3 x + a 4 ; the remainder is 0. x 5 - ax 4 Check : (x - a)(x 4 + ax 3 + a 2 x 2 + a 3 x + a 4 ) + 0 = x 5 + ax 4 + a 2 x 3 + a 3 x 2 + a 4...
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This homework help was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

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