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§8.1 Adding and Subtracting Polynomials

§8.1 Adding and Subtracting Polynomials. Simplify each expression. 1. 6 t + 13 t 2. 5 g + 34 g 3. 7 k – 15 k 4. 2 b – 6 + 9 b 5. 4 n 2 – 7 n 2 6. 8 x 2 – x 2. Warm-up. 6 t + 13 t = (6 + 13) t = 19 t 5 g + 34 g = (5 + 34) g = 39 g 7 k – 15 k = (7 – 15) k = –8 k

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§8.1 Adding and Subtracting Polynomials

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  1. §8.1 Adding and Subtracting Polynomials

  2. Simplify each expression. 1. 6t + 13t2. 5g + 34g 3. 7k – 15k4. 2b – 6 + 9b 5. 4n2 – 7n26. 8x2 – x2 Warm-up

  3. 6t+ 13t = (6 + 13)t = 19t • 5g + 34g = (5 + 34)g = 39g • 7k – 15k = (7 – 15)k = –8k • 2b – 6 + 9b = (2 + 9)b – 6 = 11b – 6 • 4n2 – 7n2 = (4 – 7)n2 = –3n2 • 8x2 – x2 = (8 – 1)x2 = 7x2 Solutions

  4. Key Terms: Monomial:an expression that is a number, a variable, or a product of a number and one or more variables. Examples: 6 j -23x3y Monomial: Monomial:an expression that is a number, a variable, or a product of a number and one or more variables.

  5. Key Terms: Degree of a Monomial: Degree of a Monomial:the sum of the exponents of its variable(s). For a nonzero constant, the degree is 0. Zero has no degree.

  6. Key Terms: Polynomial:a monomial or the sum or difference of two or more monomials. Polynomial:

  7. Key Terms: Standard Form of a Polynomial:a polynomial where the degrees of its monomial terms decrease from left to right. Standard Form of a Polynomial:

  8. Key Terms: Degree of a Polynomial:is dependent on the variable in question, and is the same as the degree of the monomial with the greatest exponent. Degree of a Polynomial:

  9. Degree: 0 The degree of a nonzero constant is 0. The exponents are 1 and 3. Their sum is 4. Degree: 4 Degree: 1 6c = 6c1. The exponent is 1. Find the degree of each monomial. a. 18 b. 3xy3 Example 1: Finding the Degree of a Monomial c. 6c

  10. Place terms in order. 7x – 2 3x5 – 2x5 + 7x – 2 Place terms in order. Combine like terms. x5 + 7x – 2 Write each polynomial in standard form. Then name each polynomial by its degree and the number of its terms. a. –2 + 7x linear binomial b. 3x5 – 2 – 2x5 + 7x Example 3: Classifying Polynomials fifth degree trinomial

  11. 6x2 + 3x + 7 2x2 – 6x – 4 8x2 – 3x + 3 Group like terms. Then add the coefficients. (6x2 + 3x + 7) + (2x2 – 6x – 4) = (6x2 + 2x2) + (3x – 6x) + (7 – 4) Simplify (6x2 + 3x + 7) + (2x2 – 6x – 4). Method 1:Add vertically. Line up like terms. Then add the coefficients. Method 2:Add horizontally. Example 4: Adding Polynomials = 8x2 – 3x + 3

  12. (2x3 + 4x2 – 6) Line up like terms. –(5x3 + 2x – 2) 2x3 + 4x2– 6 Add the opposite. –5x3- 2x+2 –3x3 + 4x2– 2x – 4 Simplify (2x3 + 4x2 – 6) – (5x3 + 2x – 2). Method 1:Subtract vertically. Line up like terms. Then add the coefficients. Example 5: Subtracting Polynomials

  13. = (2x3 – 5x3) + 4x2 – 2x + (–6 + 2)Group like terms. = –3x3 + 4x2 – 2x – 4Simplify. Example 5: Subtracting Polynomials Method 2: Subtract horizontally. (2x3 + 4x2 – 6) – (5x3 + 2x – 2) = 2x3 + 4x2 – 6 – 5x3– 2x+ 2 Write the opposite of each term in the polynomial being subtracted.

  14. Assignment: Pg. 490 16-42 Left

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