CHAPTER 6 6-4 Adding and subtracting polynomials.
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Transcript of CHAPTER 6 6-4 Adding and subtracting polynomials.
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CHAPTER 6 6-4 Adding and subtracting polynomials
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Objectives Add and subtract 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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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
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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.
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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
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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
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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
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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
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Example 2: Adding Polynomials
Add A. (4m2 + 5) + (m2 – m + 6) B. (10xy + x) + (–3xy + y) C.
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Check It Out! Example 2
Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).
Solution: 12a3 + 15a2 – 16a
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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
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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.
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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
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Check It Out! Example 3
Subtract. (2x2 – 3x2 + 1) – (x2 + x + 1) Solution: –2x2 – x
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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.
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Solution (3x2 + 7x – 5)
8x2 + 3x + 6+(5x2 – 4x + 11)
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Student guided practice Do even problems 1-12 in your book
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Homework Do even problems 16-30 in your book
page 417
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Closure Today we learned about adding and
subtracting polynomials Next class we are going to learn about
multiplying and dividing polynomials