Adding and Subtracting Polynomials 6 4 Polynomials Warm
Adding and Subtracting Polynomials 6 -4 Polynomials Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Algebra Holt Algebra 1 1 Algebra 1
6 -4 Adding and Subtracting Polynomials Warm Up 01/06/17 Simplify each expression by combining like terms. 1. 4 x + 2 x 2. 8 p – 5 p Simplify each expression. 3. 3(x + 4) 4. – 1(x 2 – 4 x – 6) Holt Mc. Dougal Algebra 1
6 -4 Adding and Subtracting Polynomials Essential Objective Add and subtract polynomials. Holt Algebra 1
6 -4 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. Holt Algebra 1
6 -4 Adding and Subtracting Polynomials Example: Adding and Subtracting Monomials A. 12 p 3 + 11 p 2 + 8 p 3 20 p 3 + 11 p 2 B. 5 x 2 – 6 – 3 x + 8 5 x 2 – 3 x + 2 Holt Algebra 1 Identify like terms. Combine like terms.
6 -4 Adding and Subtracting Polynomials I do…. C. t 2 + 2 s 2 – 4 t 2 – s 2 Identify like terms. t 2 – 4 t 2 + 2 s 2 – 3 t 2 + s 2 D. 10 m 2 n + 4 m 2 n – 8 m 2 n 6 m 2 n Holt Algebra 1 Identify like terms.
6 -4 Adding and Subtracting Polynomials Remember! Like terms are constants or terms with the same variable(s) raised to the same power(s). Holt Algebra 1
6 -4 Adding and Subtracting Polynomials We d 0. . Add or subtract. a. 2 s 2 + 3 s 2 + s 5 s 2 + s b. 4 z 4 – 8 + 16 z 4 + 2 4 z 4 + 16 z 4 – 8 + 2 20 z 4 – 6 Holt Algebra 1
6 -4 Adding and Subtracting Polynomials You do…. Add or subtract. c. 2 x 8 + 7 y 8 – x 8 – y 8 x 8 + 6 y 8 d. 9 b 3 c 2 + 5 b 3 c 2 – 13 b 3 c 2 b 3 c 2 Holt Algebra 1
6 -4 Adding and Subtracting Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: 5 x 2 + 4 x + 1 + 2 x 2 + 5 x + 2 7 x 2 + 9 x + 3 In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms. (5 x 2 + 4 x + 1) + (2 x 2 + 5 x + 2) = (5 x 2 + 2 x 2) + (4 x + 5 x) + (1 + 2) = 7 x 2 + 9 x + 3 Holt Algebra 1
6 -4 Adding and Subtracting Polynomials Example: Adding Polynomials Holt Algebra 1
6 -4 Adding and 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 signs of each term: Change the signs and proceed to addition! –(2 x 3 – 3 x + 7)= – 2 x 3 + 3 x – 7 Holt Algebra 1
6 -4 Adding and Subtracting Polynomials Example: Subtracting Polynomials (x 3 + 4 y) – (2 x 3) (x 3 + 4 y) + (– 2 x 3) Rewrite subtraction as addition of the opposite. (x 3 + 4 y) + (– 2 x 3) (x 3 – 2 x 3) + 4 y –x 3 + 4 y Holt Algebra 1 Combine like terms.
6 -4 Adding and Subtracting Polynomials We do…. Subtract. (– 10 x 2 – 3 x + 7) – (x 2 – 9) (– 10 x 2 – 3 x + 7) + (–x 2 + 9) – 10 x 2 – 3 x + 7 –x 2 + 0 x + 9 – 11 x 2 – 3 x + 16 Holt Algebra 1
6 -4 Adding and Subtracting Polynomials You do…. Subtract. (9 q 2 – 3 q) – (q 2 – 5) (9 q 2 – 3 q) + (–q 2 + 5) 9 q 2 – 3 q + 0 + − q 2 – 0 q + 5 8 q 2 – 3 q + 5 Holt Algebra 1
6 -4 Adding and Subtracting Polynomials Example: 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 3 x 2 + 7 x – 5 and the area of plot B can be represented by 5 x 2 – 4 x + 11. Write a polynomial that represents the total area of both plots of land. (3 x 2 + 7 x – 5) + (5 x 2 – 4 x + 11) 8 x 2 + 3 x + 6 Holt Algebra 1 Plot A. Plot B. Combine like terms.
6 -4 Adding and Subtracting Polynomials Lesson Quiz Add or subtract. 1. 7 m 2 + 3 m + 4 m 2 2. (r 2 + s 2) – (5 r 2 + 4 s 2) 3. (10 pq + 3 p) + (2 pq – 5 p + 6 pq) 4. (14 d 2 – 8) + (6 d 2 – 2 d +1) 5. (2. 5 ab + 14 b) – (– 1. 5 ab + 4 b) Holt Algebra 1 01/06/17
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