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Adding and Subtracting Polynomials ALGEBRA 1 LESSON 9-1 (For help, go to Lesson 1-7.) Simplify each expression. 1.6t + 13t2.5g + 34g 3.7k – 15k4.2b – 6 + 9b 5.4n 2 – 7n 2 6.8x 2 – x 2 4-2

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Adding and Subtracting Polynomials ALGEBRA 1 LESSON 9-1 1.6t + 13t = (6 + 13)t = 19t2.5g + 34g = (5 + 34)g = 39g 3.7k – 15k = (7 – 15)k = –8k4.2b – 6 + 9b = (2 + 9)b – 6 = 11b – 6 5.4n 2 – 7n 2 = (4 – 7)n 2 = –3n 2 6.8x 2 – x 2 = (8 – 1)x 2 = 7x 2 Solutions 4-2

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ALGEBRA 1 LESSON 9-1 Adding and Subtracting Polynomials Find the degree of each monomial. a. 18 b. 3xy 3 c. 6c 4-2 The degree of a nonzero constant is 0.Degree: 0 The exponents are 1 and 3. Their sum is 4.Degree: 4 6c = 6c 1. The exponent is 1.Degree: 1

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Adding and Subtracting Polynomials ALGEBRA 1 LESSON 9-1 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. 3x 5 – 2 – 2x 5 + 7x x 5 + 7x – 2Combine like terms. fifth degree trinomial Place terms in order. 3x 5 – 2x 5 + 7x – 2 Place terms in order. 7x – 2 4-2

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Adding and Subtracting Polynomials ALGEBRA 1 LESSON 9-1 Simplify (6x 2 + 3x + 7) + (2x 2 – 6x – 4). Method 1: Add vertically. Line up like terms. Then add the coefficients. 6x 2 + 3x + 7 2x 2 – 6x – 4 8x 2 – 3x + 3 Method 2: Add horizontally. Group like terms. Then add the coefficients. (6x 2 + 3x + 7) + (2x 2 – 6x – 4) = (6x 2 + 2x 2 ) + (3x – 6x) + (7 – 4) = 8x 2 – 3x + 3 4-2

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Adding and Subtracting Polynomials Simplify (2x 3 + 4x 2 – 6) – (5x 3 + 2x – 2). ALGEBRA 1 LESSON 9-1 Method 1: Subtract vertically. Line up like terms. Then add the coefficients. (2x 3 + 4x 2 – 6)Line up like terms. –(5x 3 – 2x – 2) 2x 3 + 4x 2 – 6Add the opposite. –5x 3 – 2x + 2 –3x 3 + 4x 2 – 2x – 4 4-2

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Adding and Subtracting Polynomials (continued) ALGEBRA 1 LESSON 9-1 Method 2: Subtract horizontally. = 2x 3 + 4x 2 – 6 – 5x 3 – 2x + 2Write the opposite of each term in the polynomial being subtracted. = (2x 3 – 5x 3 ) + 4x 2 – 2x + (–6 + 2)Group like terms. = –3x 3 + 4x 2 – 2x – 4Simplify. (2x 3 + 4x 2 – 6) – (5x 3 + 2x – 2) 4-2

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Adding and Subtracting Polynomials ALGEBRA 1 LESSON 9-1 Simplify each expression. Then name each polynomial by its degree and number of terms. 1.–4 + 3x – 2x 2 2.2b 2 – 4b 3 + 6 3.(2x 4 + 3x – 4) + (–3x + 4 + x 4 ) 4.(–3r + 4r 2 – 3) – (4r 2 + 6r – 2) –2x 2 + 3x – 4; quadratic trinomial –4b 3 + 2b 2 + 6; cubic trinomial 3x 4 ; fourth degree monomial –9r – 1; linear binomial 4-2

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