# Division of Polynomials Homework Solutions Feb 19 th Assignment.

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Division of Polynomials Homework Solutions Feb 19 th Assignment

Long division x 2 – 7x + 2 + 1.) x + 3 x 3 – 4x 2 – 19x + 9 x 3 + 3x 2 (change signs) - 7x 2 – 19x - 7x 2 – 21 x (change signs) 2x + 9 2x + 6 (change signs) 3 Synthetic Division-3 1 -4 -19 9 -3 21 -6 1 -7 2 3 x 2 – 7x + 2 + x 2 x # R

Long division – ADD in the 0x 2 term 4x 2 + 28x - 4 2.) x - 7 4x 3 + 0x 2 – 200x + 28 4x 3 - 28x 2 (change signs) + 28x 2 – 200x + 28x 2 – 196x (change signs) -4x + 28 -4x + 28 (change signs) 0 Synthetic Division7 4 0 -200 28 28 196 -28 4 28 -4 0 4x 2 + 28x - 4 x 2 x # R

Long division 5x + 4 + 3.) 2x - 3 10x 2 – 9x + 7 10x 2 – 15x (change signs) 8x + 7 8x – 12 (change signs) 19 Cannot do synthetic division with this problem.

Long division 4x 2 – 1x - 5 - 4.) 2x + 3 8x 3 + 10x 2 – 13x - 20 8x 3 + 12x 2 (change signs) -2x 2 – 13x -2x 2 – 3x (change signs) -10x - 20 -10x - 15 (change signs) -5 Synthetic Division cannot be done with this problem

Long division ADD in 0x 2 and 0x terms!!! x 2 + 9x + 81 5.) x - 9 x 3 + 0x 2 + 0x - 729 x 3 - 9x 2 (change signs) 9x 2 + 0x 9x 2 – 81x (change signs) 81x - 729 81x - 729 (change signs) 0 Synthetic Division9 1 0 0 729 9 81 -729 1 9 81 0 x 2 + 9x + 81 x 2 x # R

Long division x 2 – 3x + 2 6.) x - 4 x 3 – 7x 2 + 14x - 8 x 3 - 4x 2 (change signs) - 3x 2 + 14x - 3x 2 + 12x (change signs) 2x - 8 2x - 8 (change signs) 0 Synthetic Division 4 1 -7 14 -8 4 -12 8 1 -3 2 0 x 2 – 3x + 2 x 2 x # R

Long division x 2 – 4x + 5 + 7.) x + 2 x 3 – 2x 2 – 3x + 12 x 3 + 2x 2 (change signs) - 4x 2 - 3x - 4x 2 – 8x (change signs) 5x + 12 5x + 10 (change signs) Synthetic Division-2 1 -2 -3 12 -2 8 -10 1 -4 5 2 x 2 – 4x + 5 + x 2 x # R

Long division x + 2 - 8.) x + 4 x 2 + 6x - 17 x 2 + 4x (change signs) 2x – 17 2x + 8 (change signs) -25 Synthetic Division-4 1 6 -17 -4 -8 1 2 -25 x + 2 - x # R

Long division 2x + 6 + 9.) 3x - 5 6x 2 + 8x - 4 6x 2 - 10x (change signs) 18x – 4 18x - 30 (change signs) 26 Synthetic Divisioncannot be done with this problem

Long division x 2 + 3x + 5 10.) x - 6 x 3 - 3x 2 – 23x + 30 x 3 - 6x 2 (change signs) 3x 2 – 23x 3x 2 – 18x (change signs) 5x + 30 5x - 30 (change signs) 0 Synthetic Division6 1 -3 -23 30 6 18 -30 1 3 5 0 x 2 + 3x + 5 x 2 x # R