©thevisualclassroom.com

Example 1: (4x3 – 5x – 6) ÷ (2x + 1)

4x3 + 0x2 – 5x – 62x + 1

2x2

4x3 + 2x2

–2x2 – 5x

– x

– 4x

(restriction)

1

2x

–2x2 – x

+ +

– 6

– 2

– 4x – 2

+ +

– 4 (remainder)

1.4 Dividing Polynomials1) Long Division

©thevisualclassroom.com

(3x3 – 2x2 + 5x – 2 ) ÷ (x2 + 3x – 1)

3x

3x3 + 9x2 – 3x –11x2 +8x

41x – 13–11x2 –33x + 11

+ +

– 11

(remainder)

x2 + 3x – 1 3x3 – 2x2 + 5x – 2

– 2

3 2

2 2

3 2 5 2 41 13 = 3 11

3 1 3 1

x x x xx

x x x x

+

Example 2:

©thevisualclassroom.com

Example 1: (2x2 – 5x – 9) ÷ (x – 2) (x

2 – 5 – 9

24

– 1– 2

– 11

Ans: 2x – 1 R – 11

(write only the coefficients)bring down the first term

multiplyadd

22(opposite sign)

2) Synthetic Division

©thevisualclassroom.com

Example 2: (2x3 + 5x – x2 – 6) ÷ (x + 2)

(x

2 – 1 + 5 – 6- 2

2

– 4

– 5

10

15

Ans: 2x2 – 5x +15 R – 36

– 30

– 36

(2x3 – x2 + 5x – 6)

– 2(opposite sign)

©thevisualclassroom.com

Example 3: (4x2 – 6) ÷ (2x + 1)

4 0 – 6

4– 2– 2

1– 5

12

2x

1

2x (4x2 + 0x – 6)

1

2

Ans: 2x – 1 R – 5

2

1

2

(opposite sign)

2

©thevisualclassroom.com

Example 4: (3x2 + 5x – 6) ÷ (3x – 1)

3 5 – 6

3 1 6

2– 4

13

3x

1

3x

1

3

Ans: x + 2 R – 4

3

1

3

3