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Section 9-1 Adding and Subtracting Polynomials SPI 12C: add and subtract algebraic expressions Objectives: Classify a polynomial by degree and number of terms. Simplify polynomials by adding and subtracting like terms. Write polynomials in standard form. Polynomial: sum or difference of 2 or more monomials. Monomial: one term Binomial: two terms (separated by a + or – sign) Trinomial: three terms (separated by a + or – sign) Degree of a monomial (one term): sum of the exponents of its variables EX: 4m 3 n 2 (degree 5); 4x 2 (degree 2) Degree of a polynomial (more than one term): the degree of the monomial with the greatest exponent. EX: 4x 2 + 2x + 3 (degree is 2)

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Naming Polynomials Always write polynomials in standard form: - degrees of terms decrease from left to right Degree of polynomial is the monomial with the greatest exponent Name Polynomials based of degree and number of monomials How would you name the polynomial 3x 4 + 5x 2 – 1? Fourth degree trinomial 3x 4 + 5x 2 – 1

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Find the degree of each monomial. a. 18 b. 3xy 3 c. 6c The degree of a nonzero constant is 0.Degree: 0 The exponents are 1 and 3.Degree: 4 6c = 6c 1. The exponent is 1.Degree: 1 Write the polynomial in standard form. Then name the polynomial by its degree and the number of its terms. –2 + 7x linear binomial Place terms in order. 7x – 2 Naming Polynomials

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Adding and Subtracting Polynomials 3x 2 and x 2 are like terms 3x 2 and x are NOT like terms Negative sign outside parenthesis: distribute negative sign to each term on the inside of the parenthesis – (5x 2 + 2x – 2) = – 5x 2 – 2x + 2 Combining Like Terms

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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) = = 8x 2 – 3x + 3 Adding and Subtracting Polynomials Two Methods Vertical method Horizontal method (6x 2 + 2x 2 ) + (3x – 6x) + (7 – 4)

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Simplify (2x 3 + 4x 2 – 6) – (5x 3 + 2x – 2). 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 – 6 Add the opposite. –5x 3 – 2x + 2 –3x 3 + 4x 2 – 2x – 4 Adding and Subtracting Polynomials

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Method 2: Subtract horizontally = 2x 3 + 4x 2 – 6 – 5x 3 – 2x + 2 Distribute negative = (2x 3 – 5x 3 ) + (4x 2 – 2x) + (–6 + 2) Group like terms. = –3x 3 + 4x 2 – 2x – 4 Simplify (2x 3 + 4x 2 – 6) – (5x 3 + 2x – 2) Adding and Subtracting Polynomials

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