Notes for Lesson 7-6: Adding and Subtracting Polynomials

advertisement

Notes for Lesson 7-6: Adding and Subtracting Polynomials

7-6.1 – Adding and Subtracting Monomials

Earlier in the year, we added and subtracted like terms. We said like terms were terms that had the same variables at the same power. These term were also monomials. So to add monomials we simply add like terms.

Examples: Add or subtract.

15 m

3 

6 m

2 

2 m

3

17 m

3 

6 m

2

3

 x

4

2 x

2

5

7

17 x

2 

12 0 .

9 y

5

1 .

5 y

5

0 .

4 y

5 

0 .

5 x

5  y

5

 x

5

7-6.2 – Adding Polynomials

To add polynomials we can either line up the polynomials vertically by like terms or we can use the associative and commutative properties to collect like terms and add horizontally.

Examples: Add.

( 2 x

2  x )

( x

2 

3 x

1 )

(

2 ab

 b )

( 2 ab

 a )

( 4 x

2 

3 x

6 )

( 2 x

2

2 x

2  x x

2 

3 x

1

2 ab

2 ab

 b

 a

4 x

2 

3 x

6

2 x

2 

4 x

5

4 x

5 )

3 x

2 

2 x

1 0 b

 a 6 x

2  x

1 or

( 2 x

2  x

2

)

(

 x

3 x )

(

1 ) or

(

2 ab

2 ab )

( b )

( a ) b

 a or

( 4 x

2 

2 x

2

)

( 3 x

4 x )

(

6

5 )

3 x

2 

2 x

1

7-6.3 – Subtracting Polynomials

6 x

2  x

1

To subtract polynomials you must remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial you must write the opposite of each term in the polynomial. Then add the polynomials together using the above method.

Examples: Subtract.

( a 4 

2 a )

( 3 a 4 

3 a

1 ) ( 3 x

2 

2 x

8 )

( x

2 

4 ) ( 2 x

2 

3 x

2 

1 )

( x

2  x

1 )

( a

4 

2 a )

(

3 a

4 

3 a

1 ) ( 3 x

2 

2 x

8 )

(

 x

2 

4 ) (

 x

2 

1 )

(

 x

2  x

1 ) a

4 

2 a 3 x

2 

2 x

8

 x

2 

1

 

3 a

4 

3 a

1

2 a 4  a

1

  x

2 

4

2 x

2 

2 x

12

  x

2  x

1

2 x 2  x or

( a

4 

3 a

4

)

(

2 a

3 a )

(

1 )

2 a

4  a

1 or

( 3 x

2  x

2

)

(

2 x )

( 8

4 )

2 x

2 

2 x

12 or

(

 x

2  x

2

)

(

 x )

( 1

1 )

2 x

2  x

7-6.4 – Business Application

The profits of two different manufacturing plants can be modeled as shown, where x is the number of units produced at each plant.

0 .

Eastern Plant

03 x

2 

25 x

1500

0 .

Western Plant

02 x

2 

21 x

1700

Write a polynomial that represents the difference of the profits at the Eastern plant and the Western plant.

(

0 .

03 x

2 

25 x

1500 )

(

0 .

02 x

2 

21 x

1700 )

(

0 .

03 x

2 

25 x

1500 )

( 0 .

02 x

2 

21 x

1700 )

0 .

03 x

2 

25 x

1500

0 .

02 x

2 

21 x

1700

0 .

01 x

2 

4 x

200

Do Practice B #’s 7, 12, 13, 14

Download