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Chapter 9.1 Notes: Add and Subtract Polynomials Goal: You will add and subtract polynomials.

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A monomial is a number, a variable with a positive integer exponent, or the product of a number and one or more variables with positive integer exponents. Monomials Not a Monomial 10 5 + x 3x 2 / n ½ ab 2 4 a -1.8m 5 x -1

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The degree of a monomial is the sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0. MonomialDegree 10 3x ½ ab 2 -1.8m 5 7x 2 y 5 -2x 0

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A polynomial is a monomial or a sum of monomials, each called a term of the polynomial. The degree of a polynomial is the greatest degree of its terms. When a polynomial is written so that the exponents of a variable decrease from left to right, the coefficient of the first term is called the leading coefficient. 2x 3 + x 2 – 5x + 12

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Ex.1: Write 15x – x 3 + 3 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial. Ex.2: Write 3b 3 – 4b 4 + b2 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.

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Binomials and Trinomials A polynomial with two terms is called a binomial. i.e. i.e. i.e. A polynomial with three terms is called a trinomial. i.e. i.e. i.e.

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Ex.3: Tell whether the expression is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial. ExpressionIs it a polynomial?Classify by degree and number of terms 9 2x 2 + x – 5 6n 4 – 8 n n -2 – 3 7bc 3 + 4b 4 c

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Ex.4: Find the sum or difference. a. -3b 2 + 7b 2 b. 2xy – 5xy c. 6x 2 z + 13x 2 z d. -25b 2 + 18b 2 Adding Polynomials (3x 2 + x – 6) + (x 2 + 4x + 10) Method 1: Method 2:

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Ex.5: Find the sum. a. (-2x 2 + 3x – x 3 ) + (3x 2 + x 3 – 12) b. (5x 3 + 4x 2 – 2x) + (4x 2 + 3x 3 – 6) c. (5m 2 – m + 2) + (-3m 2 + 10m + 7) d. (7k 2 + 2k – 6) + (3k 2 – 11k – 8) Subtracting Polynomials (8x2 – 7x + 12) – (2x2 – 4x – 3) Method 1: Method 2:

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Ex.6: Find the difference. a. (4x 2 – 3x + 5) – (3x 2 – x – 8) b. (2c 2 – 8) – (3c 2 – 4c + 1) c. (4x 2 – 7x) – (5x 2 + 4x – 9) d. (8x 2 – 4x + 12) – (-2x 2 – 7x – 5) Ex.7: Find the sum or difference. a. (7m 2 + 8m – 3) + (-3m 2 – 4m + 11) b. (-6x 2 – 7x – 9) – (12x 2 + 8x – 5) c. (4x 2 + 5x – 6) + (7x 2 + 4x – 3) d. (12x 2 – 7x – 10) – (-12x 2 + 9x – 6)

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