Dividing Polynomials

Divide Polynomials using Long Division and Synthetic Division.

#1 Divide a polynomial by a monomial.

2

564 3 xx

2

5

2

6

2

4 3

xx

2

532 3 xx

#2 Divide a polynomial by a monomial.

x

xxx

2

462 23

x

x

x

x

x

x

2

4

2

6

2

2 23

232 xx

#3 Divide the following numbers.

13

5733

5733134

5253

4

5213

1 Check

13

441

5733

130

Long Division

1. Divide the first term of the numerator by the first term of the denominator.

2. Distribute your quotient by the entire polynomial in the denominator.

3. Distribute a negative by through your product.

#4 Divide the following numbers (Long Division)

11

8034

8034117

7733

3

3304

0

04 Remainder

11

4730

#5 Dividing a polynomial by a polynomial (Long Division)

2

822

x

xx

822 2 xxxx

xx 22 x4 8

4

84 x0

Check

)2)(4( xx

8422 xxx

822 xx

x

x2

)2(xx

x

x4 )2(4 x

36x

#6 Dividing a polynomial by a polynomial (Long Division)

7

42133

36

x

xx

3x

36 7xx 42

6

426 3 x0

Check

)6)(7( 33 xx

4276 336 xxx

4213 36 xx

)7( 33 xx

)7(6 3x

42137 363 xxx

3

6

x

x

3

36

x

x

#7 Dividing a polynomial by a polynomial (Long Division)

1

124

x

xx

1001 234 xxxxx

3x

34 xx 3x 2x

2x

23 xx 22x x0

x2 x2

xx 22 2 x2 1

2

12 x22 x3

1

3

x

#8 Dividing a polynomial by a polynomial (Long Division)

yy

yyy

523

19730152

23

7301915253 232 yyyyyy5

yyy 102515 23 26y y20

2

4106 2 yy11y10

7

253

11102

yy

y