# ©thevisualclassroom.com Example 1: (4x 3 – 5x – 6) ÷ (2x + 1) 4x 3 + 0x 2 – 5x – 6 2x + 1 2x22x2 4x 3 + 2x 2 –2x 2 – 5x – x – 4x (restriction) –2x 2 –

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©thevisualclassroom.com Example 1: (4x 3 – 5x – 6) ÷ (2x + 1) 4x 3 + 0x 2 – 5x – 6 2x + 1 2x22x2 4x 3 + 2x 2 –2x 2 – 5x – x – 4x (restriction) –2x 2 – x + + – 6 – 2 – 4x – 2 + + – 4 (remainder) 1.4 Dividing Polynomials 1) Long Division

©thevisualclassroom.com (3x 3 – 2x 2 + 5x – 2 ) ÷ (x 2 + 3x – 1) 3x3x 3x 3 + 9x 2 – 3x –11x 2 +8x 41x – 13 –11x 2 –33x + 11 + + – 11 (remainder) x 2 + 3x – 13x 3 – 2x 2 + 5x – 2 – 2 + Example 2:

©thevisualclassroom.com Example 1: (2x 2 – 5x – 9) ÷ (x – 2) (x   2 – 5 – 9 2 4 – 1 – 2 – 11 Ans: 2x – 1 R – 11 (write only the coefficients) bring down the first term multiply add 2 2 (opposite sign) 2) Synthetic Division

©thevisualclassroom.com Example 2: (2x 3 + 5x – x 2 – 6) ÷ (x + 2) (x  2 – 1 + 5 – 6 - 2 2 – 4 – 5 10 15 Ans: 2x 2 – 5x +15 R – 36 – 30 – 36 (2x 3 – x 2 + 5x – 6) – 2 (opposite sign)

©thevisualclassroom.com Example 3: (4x 2 – 6) ÷ (2x + 1) 4 0 – 6 4 – 2– 2 – 2 1 – 5 (4x 2 + 0x – 6) Ans: 2x – 1 R – 5 (opposite sign)

©thevisualclassroom.com Example 4: (3x 2 + 5x – 6) ÷ (3x – 1) 3 5 – 6 3 1 6 2 – 4 Ans: x + 2 R – 4

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