4.8b S KM & PP 1

Division of Polynomials

4.8b S KM & PP 2

Division of Polynomials

First, let’s review the symbols that represent the division problem:

“a divided by b”

ba b/aba

ab

4.8b S KM & PP 3

How to Write:

“Seventeen divided by five”

517

517 /

5

17

175

4.8b S KM & PP 4

Division of Polynomials

Now let’s review the terminology for the parts of a division

problem.

Divisor

Quotient

Remainder

Dividend

Division Symbol

4.8b S KM & PP 5

Long DivisionReview the Terminology

Divisor

QuotientRemainder

DividendDivision Symbol

Equal Symbol

“Seventeen divided by five”

4.8b S KM & PP 6

Long Division

Divisor

Quotient

Remainder

DividendDivision Symbol

Equal Symbol

“Seventeen divided by five”

4.8b S KM & PP 7

Long Division

Divisor

Quotient

Fractional Remainder

Dividend

Division Symbol

“Seventeen divided by five”

4.8b S KM & PP 8

12 4 17

Long DivisionStudy the steps!

3 4

3 65748

9

34912

4.8b S KM & PP 9

Polynomial Long Division:Steps

The same steps are used to divide a polynomial by a binomial:

1. Divide

2. Multiply

3. Subtract

4. Bring Down

4.8b S KM & PP 10

x-2 x2 - 13x + 22

Example 1:2

22132

xxx

xx2

x

)x(x 2

xxxx 213 22

Divide

Multiply

Subtract

Bring Down

+ 22

xx11

Divide

xx 22

x11

11

)x( 211Multiply

2211 x

0Subtract

22112211 xx

4.8b S KM & PP 11

x - 11

x-2 x2 - 13x + 22

x2 - 2x

-11x + 22

-11x + 22

0

Example 1:2

22132

xxx

To check our answer, multiply the divisor and the quotient:

(x - 2)(x - 11) = x2 - 13x + 22

4.8b S KM & PP 12

3x-2 12x2 + 13x

- 14

Example 2:

xx

3

12 2

x4

)x(x 234

xxxx 8121312 22

Divide

Multiply

Subtract

Bring Down

-14

xx

3

21Divide

xx 812 2

x21

7

)x( 237Multiply

1421 x

0Subtract 14211421 xx

23

141312 2

xxx

4.8b S KM & PP 13

4x + 7

3x-2 12x2 + 13x

- 14

12x2 - 8x

21x - 14

21x - 14

0

Example 2:

To check our answer, multiply the divisor and the quotient:

(3x - 2)(4x + 7) = 12x2 + 13x -14

23

141312 2

xxx

4.8b S KM & PP 14

Example 3:

-3

3x - 4 2x+1

2x+1

6x2 - 5x - 7

6x2 + 3x

-8x - 7

-8x - 4

- 3

12

756 2

xxx

xx

2

6 2

x3xx

2

84

4.8b S KM & PP 15

Example 3:

-3

3x - 4 2x+1

2x+1

6x2 - 5x - 7

6x2 + 3x

-8x - 7

-8x - 4

- 3

12

756 2

xxx

Check: divisor times quotient plus

remainder

(2x+1)(3x-4) + (-3) =

6x2 - 8x + 3x - 4 – 3 = 6x2 - 5x -7

4.8b S KM & PP 16

x2 + x + 1

x-1 x3 + 0x2

+ 0x1 - 1

x3 - x2

x2 + 0x

x2 - x

x - 1

x - 1

0

Example 4:1

13

xx

xx3

2xxx2

x xx

1

Remember to put in place holders for the missing powers of x.

4.8b S KM & PP 17

That’s All for Now!