Dividing Polynomials

1
Dividing Polynomials

• Using Long Division

2
Terminology

• Dividend Numerator
• Divisor Denominator

Quotient Remainder
3
Steps to Divide

1. Divide
2. Multiply
3. Subtract
4. Bring Down
5. Shampoo, Rinse, Repeat (if necessary)

4
Quick Remembrance

• Set up to divide.
• Divide 7 by 5.
• Multiply 1 by 5.
• Subtract down (75)
• Bring Down 5.
• Divide 25 by 5.
• Multiply 5 by 5.
• Subtract Down (2525)
• Bring Down 5.
• Divide 05 by 5.
• Multiply 1 by 5.
• Subtract Down (55)

5
1
1
5
5
25
5
5
Remainder
5
x
1

• Divide x2 by x, which is x.
• Multiply x by x 3, which is x2 3x.
• Subtract
• (x2 4x) - (x2 3x),
• which is x.
• Bring down the 3.
• Repeat using x 3 as our new divisor.

0

• Divide x by x, which is 1.
• Multiply 1 by x 3, which is x 3.
• Subtract
• (x 3) - (x 3),
• which is 0 (remainder).

6
x
2

• Divide x2 by x, which is x.
• Multiply x by x 1, which is x2 x.
• Subtract
• (x2 3x) (x2 x),
• which is 2x.
• Bring down the -6.
• Repeat using 2x 6 as our new divisor.

-8

• Divide x by x, which is 2.
• Multiply 2 by x 1, which is 2x 2.
• Subtract
• (2x 6) (2x 2),
• which is -8 (remainder).

7

1. Divide
2. Multiply
3. Subtract
4. Bring Down
5. Repeat (if necessary)

8

1. Divide
2. Multiply
3. Subtract
4. Bring Down
5. Repeat (if necessary)

Remainder
9

1. Divide
2. Multiply
3. Subtract
4. Bring Down
5. Repeat (if necessary)

Remainder
10

1. Divide
2. Multiply
3. Subtract
4. Bring Down
5. Repeat (if necessary)

11

1. Divide
2. Multiply
3. Subtract
4. Bring Down
5. Repeat (if necessary)