3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6x

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Presentation transcript:

3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6x D M S B 3x + 2 6x3 - 5x2 – 12x – 4 6x3 + 4x2 -9x2 – 12x -9x2 – 6x – 6x – 4 – 6x – 4 Check: (3x + 2)(2x2 – 3x – 2) = 6x3 – 9x2 – 6x + 4x2 – 6x – 4 6x3 – 5x2 – 12x – 4

2x – 1 4x3 – 8x2 + 5x – 8 2x2 – 3x + 1 4x3 – 2x2 -6x2 + 5x -6x2 + 3x 7 (2x – 1) + 1 – 2x – 1 4x3 – 8x2 + 5x – 8 4x3 – 2x2 -6x2 + 5x -6x2 + 3x 2x – 8 2x – 1 - 7 remainder Check: (2x – 1)(2x2 – 3x + 1) = 4x3 – 6x2 + 2x – 2x2 + 3x – 1 = 4x3 – 8x2 + 5x – 1 Add remainder -7 = 4x3 – 8x2 + 5x – 8

x2 + 3x 5x4 + 18x3 + 10x2 +3x 5x2 + 3x + 1 5x4 + 15x3 3x3 + 10x2 3x3

5x4 + 18x3 + 10x2 +3x 5x2 + 3x + 1 Factor: One factor is x2 + 3x Divide to find that the other factor is: 5x2 + 3x + 1

2 3 1 (3x3 + 8x2 + 5x – 7)  (x + 2) -2 3 8 5 -7 -6 -4 -2 3 2 1 -9 – Synthetic Division (3x3 + 8x2 + 5x – 7)  (x + 2) -2 3 8 5 -7 -6 -4 -2 3 2 1 -9 remainder 9 x + 2 2 3 1 – answer x2 + x +

(2x4 – 6x3 + x2 – 3x – 3)  (x – 3) 3 2 -6 1 -3 -3 6 3 2 1 -3 2x3 Synthetic Division (2x4 – 6x3 + x2 – 3x – 3)  (x – 3) 3 2 -6 1 -3 -3 6 3 2 1 -3 remainder answer 2x3 + 0x2 + 1x + 0 3 (x – 3) 2x3 + x –

Synthetic Division (x4 – 2x3 – 70x + 20)  (x – 5) 5 1 -2 -70 20 5 15 75 25 1 3 15 5 45 remainder 45 (x – 5) answer x3 + 3x2 + 15x + 5 +

(4x3 – 8x2 + 3x – 8)  (2x – 1) 2 -4 -4 1 2 -3 -4 2x2 – 3x – Synthetic Division (4x3 – 8x2 + 3x – 8)  (2x – 1) 1 2 3 2 2 -4 -4 -3 2 1 2 -3 -4 remainder 4 (2x – 1) answer 2x2 – 3x –

( 6x2 – x – 7)  (3x + 1) 2 2 -1 -2 2x – 1 – Synthetic Division 1 3 2 -7 3 2 -2 3 1 3 2 -1 -2 remainder answer 2 (3x + 1) 2x – 1 –