chapter 6 6-4 adding and subtracting polynomials

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CHAPTER 6 6-4 Adding and subtracting polynomials

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Adding and subtracting polynomials  Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

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Page 1: CHAPTER 6 6-4 Adding and subtracting polynomials

CHAPTER 6 6-4 Adding and subtracting polynomials

Page 2: CHAPTER 6 6-4 Adding and subtracting polynomials

Objectives Add and subtract polynomials.

Page 3: CHAPTER 6 6-4 Adding and subtracting polynomials

Adding and subtracting polynomials Just as you can perform operations on

numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

Page 4: CHAPTER 6 6-4 Adding and subtracting polynomials

Example 1: Adding and Subtracting Monomials

Add or subtract. A. 12p3 + 11p2 + 8p3 Solution: 12p3 + 11p2 + 8p3 Identify like terms. 12p3 + 8p3 + 11p2 Rearrange terms so

that like terms are together. 20p3 + 11p2 Combine like terms

Page 5: CHAPTER 6 6-4 Adding and subtracting polynomials

Example #1 B. 5x2 – 6 – 3x + 8 Solution 5x2 – 6 – 3x + 8 Identify like terms. 5x2 – 3x + 8 – 6 Rearrange terms so

that like terms are together.

5x2 – 3x + 2 Combine like terms.

Page 6: CHAPTER 6 6-4 Adding and subtracting polynomials

Example#1 Add or subtract. C. t2 + 2s2 – 4t2 – s2 t2 + 2s2 – 4t2 – s2 Identify like terms. t2 – 4t2 + 2s2 – s2 Rearrange terms so

that like terms are together. –3t2 + s2 Combine like terms

Page 7: CHAPTER 6 6-4 Adding and subtracting polynomials

Check it out!! Add or subtract. a. 2s2 + 3s2 + s Solution: 5s2 + s b. 4z4 – 8 + 16z4 + 2 Solution: 20z4 – 6 c. 2x8 + 7y8 – x8 – y8 Solution: x8 + 6y8

Page 8: CHAPTER 6 6-4 Adding and subtracting polynomials

Adding polynomials Polynomials can be added in either

vertical or horizontal form. In vertical form, align the like terms and

add:

5x2 + 4x + 1+ 2x2 + 5x + 2

7x2 + 9x + 3

Page 9: CHAPTER 6 6-4 Adding and subtracting polynomials

In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms.

(5x2 + 4x + 1) + (2x2 + 5x + 2) (5x2 + 2x2) + (4x + 5x) + (1 + 2)

= 7x2 + 9x + 3

Page 10: CHAPTER 6 6-4 Adding and subtracting polynomials

Example 2: Adding Polynomials

Add A. (4m2 + 5) + (m2 – m + 6) B. (10xy + x) + (–3xy + y) C.

Page 11: CHAPTER 6 6-4 Adding and subtracting polynomials

Check It Out! Example 2

Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).

Solution: 12a3 + 15a2 – 16a

Page 12: CHAPTER 6 6-4 Adding and subtracting polynomials

Subtracting polynomials To subtract polynomials, 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:

–(2x3 – 3x + 7)= –2x3 + 3x – 7

Page 13: CHAPTER 6 6-4 Adding and subtracting polynomials

Example 3A: Subtracting Polynomials

Subtract (x3 + 4y) – (2x3) Solution: Rewrite subtraction as addition of the

opposite. x3 + 4y) + (–2x3) x3 + 4y) + (–2x3) (x3 – 2x3) + 4y Group like terms together. –x3 + 4y Combine like terms.

Identify like terms.

Page 14: CHAPTER 6 6-4 Adding and subtracting polynomials

Example 3B: Subtracting Polynomials

(7m4 – 2m2) – (5m4 – 5m2 + 8) Solution: Rewrite subtraction as addition of the opposite. (7m4 – 2m2) + (–5m4 + 5m2 – 8) (7m4 – 2m2) + (–5m4 + 5m2 – 8)identify like

terms (7m4 – 5m4) + (–2m2 + 5m2) – 8 group like

terms 2m4 + 3m2 – 8

Page 15: CHAPTER 6 6-4 Adding and subtracting polynomials

Check It Out! Example 3

Subtract. (2x2 – 3x2 + 1) – (x2 + x + 1) Solution: –2x2 – x

Page 16: CHAPTER 6 6-4 Adding and subtracting polynomials

Application A farmer must add the areas of two

plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5 and the area of plot B can be represented by 5x2 – 4x + 11. Write a polynomial that represents the total area of both plots of land.

Page 17: CHAPTER 6 6-4 Adding and subtracting polynomials

Solution (3x2 + 7x – 5)

8x2 + 3x + 6+(5x2 – 4x + 11)

Page 18: CHAPTER 6 6-4 Adding and subtracting polynomials

Student guided practice Do even problems 1-12 in your book

page 417

Page 19: CHAPTER 6 6-4 Adding and subtracting polynomials

Homework Do even problems 16-30 in your book

page 417

Page 20: CHAPTER 6 6-4 Adding and subtracting polynomials

Closure Today we learned about adding and

subtracting polynomials Next class we are going to learn about

multiplying and dividing polynomials