Warm-up

1
Warm-up

• State whether each expression is a polynomial.
  If the expession is a polynomial, identify it as
  either a monomial, binomial, or trinomial and
  give its degree.
• 1. 8a2 5ab
• 2. 3x2 4x 7/x
• 3. 5x2 7x 2
• 4. 6a2b2 7ab5 6b3
• 5. w2 x - 6x

2
Warm-up

• State whether each expression is a polynomial.
  If the expession is a polynomial, identify it as
  either a monomial, binomial, or trinomial and
  give its degree.
• 1. 8a2 5ab binomial 2
• 2. 3x2 4x 7/x not a polynomial not the
  product of and variable
• 3. 5x2 7x 2 trinomial 2
• 4. 6a2b2 7ab5 6b3 trinomial 2
• 5. w2 x - 6x trinomial 2

3
Homework 6.5

1. 2
2. 3
3. 4
4. 1
5. 4
6. 4
7. 4
8. 8

9. 4 10. 5 11. 5 2x2 3x3 x4 12. 1 3x
2x2 13. - 6 5x 3x2 14. 2 x 9x2 x3 15.
- 3 4x x2 3x3 16. 2x x2 - x3 x4
4
Homework 6.5
17. 6 12x 6x2 x3 18. 21r2 7r5x r2x2
15x3 19. 5x3 - 3x2 x 4 20. - x3 x2 - x 1
21. 3x3 x2 - x 27 22. 3x3 x2 x - 17
23. x3 x - 1 24. 3x3 x2 - x 64
5
Homework 6.5
25. - x3 x 25 26. ?px3 p3 x2 px 5p
6
6.6 Adding and Subtracting Polynomials

• CORD Math
• Mrs. Spitz
• Fall 2006

7
Objectives

• After studying this lesson, you should be able to
  add and subtract polynomials.

8
Assignment

• 6.6 Worksheet

9
Application
x 3 in.

• The standard measurement for a window is the
  united inch. The united inch measurement of a
  window is equal to the sum of the length of the
  length and the width of the window. If the
  length of the window at the right is 2x 8 and
  the width is x 3 inches, what is the size of
  the window in united inches?

2x 8 in.
10
Application
x 3 in.

• The size of the window is (2x 8) (x 3)
  inches. To add two polynomials, add the like
  terms.
• (2x 8) (x - 3)
• 2x 8 x 3
• (2x x) (8 3)
• 3x 5
• The size of the window in united inches is 3x 5
  inches.

2x 8 in.
11
Application

• You can add polynomials by grouping the like
  terms together and then finding the sum (as in
  the example previous), or by writing them in
  column form.

12
Example 1 Find (3y2 5y 6) (7y2 -9)

• Method 1 Group the like terms together.
• (3y2 5y 6) (7y2 -9)
• (3y2 7y2) 5y -6 (-9)
• (3 7)y2 5y (-15)
• 10y2 5y - 15

13
Example 2 Find (3y2 5y 6) (7y2 -9) Method
2 Column form
3y2 5y 6
7y2 9
10y2 5y 15
Recall that you can subtract a rational number by
adding its additive inverse or opposite.
Similarly, you can subtract a polynomial by
adding its additive inverse.
14
To find the additive inverse of a polynomial,
replace each term with its additive inverse.
Polynomial Additive Inverse
x 2y -x 2y
2x2 3x 5 - 2x2 3x -5
- 8x 5y 7z 8x - 5y 7z
3x3 - 2x2 5x - 3x3 2x2 5x
The additive inverse of every term must be
found!!!
15
Example 2 Find (4x2 3y2 5xy) (8xy 6x2
3y2)

• Method 1 Group the like terms together.
• (4x2 3y2 5xy) (8xy 6x2 3y2)
• (4x2 3y2 5xy) ( 8xy - 6x2 - 3y2)
• (4x2 - 6x2) (5xy 8xy) (- 3y2 - 3y2)
• (4 - 6)x2 (5 8)xy (-3 - 3)y2
• -2x2 3xy -6y2
• OR WOULD YOU PREFER COLUMN FORMAT?

16
Example 2 Find (4x2 3y2 5xy) (8xy 6x2
3y2) Column format
4x2 5xy -3y2
- 6x2 8xy 3y2

First, reorder the terms so that the powers of x
are in descending order
(4x2 5xy 3y2) (6x2 8xy 3y2) THEN use
the additive inverse to change the signs
17
Example 2 Find (4x2 3y2 5xy) (8xy 6x2
3y2) Column format
4x2 5xy -3y2
- 6x2 - 8xy - 3y2
- 2x2 - 3xy - 6y2
To check this result, add -2x2 3xy -6y2 and
6x2 8xy 3y2
(4x2 5xy 3y2) This is what you should get
after you check it.
18
Example 3 Find the measure of the third side of
the triangle. P is the measure of the perimeter.

• The perimeter is the sum of the measures of the
  three sides of the triangle. Let s represent the
  measure of the third side.

3x2 2x - 1
s
8x2 8x 5
P 12x2 7x 9
19

• (12x2 7x 9) (3x2 2x - 1) (8x2 8x 5)
  s
• (12x2 7x 9) - (3x2 2x - 1) - (8x2 8x 5)
  s
• 12x2 7x 9 - 3x2 - 2x 1 - 8x2 8x - 5) s
• (12x2 - 3x2 - 8x2)( 7x - 2x 8x) (9 1 - 5)
  s
• x2 - x 5 s
• The measure of the third side is x2 - x 5.