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Lesson 8-1 Warm-Up

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**“Adding and Subtracting Polynomials” (8-1)**

What is a “monomial”? What is the “degree of a monomial”? monomial: a number, a variable, or the product of a number and one or more variables Examples: 12 y -5x2y x / 3 Note: A negative exponent is not considered a monomial Example: 3 / x , or 3x-1, is not a monomial degree of a monomial: sum of the exponents of the variables Examples:

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**Find the degree of each monomial.**

Adding and Subtracting Polynomials LESSON 8-1 Additional Examples Find the degree of each monomial. a. 18 The exponent of the variable is 0 (x0 = 1, so 18 x0 = 18 1 = 18). Degree: 0 b. 3xy3 The exponents of the variables are 1 and 3. Their sum is 4. Degree: 4 c. 6c 6c = 6c1. The exponent of the variable is 1. Degree: 1

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**“Adding and Subtracting Polynomials” (8-1)**

What is a “polynomial”? What is the “Standard Form of a Polynomial”? polynomial (poly = “many”): the sum of two or more monomials Example: standard form of a polynomial: a polynomial which is written so that the degrees of its monomial terms decreases from left to right (In other words, it goes from the term with the biggest degree to the one with the smallest degree, like a constant.) degree of a polynomial: the degree of the monomial with the greatest exponent

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**“Adding and Subtracting Polynomials” (8-1)**

How do you name, or classify, a polynomial based on its degrees or number of terms? definitions: Use the following reference table when naming, or classifying, a polynomial based on its numbers of degrees or its number of terms?

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**fifth degree trinomial**

Adding and Subtracting Polynomials LESSON 8-1 Additional Examples Write each polynomial in standard form. Then name each polynomial based on its degree and the number of its terms. a. –2 + 7x Place terms in order. 7x – 2 linear binomial b. 3x5 – 2 – 2x5 + 7x Place terms in order. 3x5 – 2x5 + 7x – 2 x5 + 7x – 2 Combine like terms. fifth degree trinomial

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**“Adding and Subtracting Polynomials” (8-1)**

How do you add or subtract polynomials? To add or subtract polynomials, combine like terms (add or subtract the coefficients of like term variables) There are two methods to adding and subtracting like terms. You can add or subtract the like terms horizontally (across) or vertically (down). Example:

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**Simplify (6x2 + 3x + 7) + (2x2 – 6x – 4).**

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

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**Simplify (2x3 + 4x2 – 6) – (5x3 + 2x – 2).**

Adding and Subtracting Polynomials LESSON 8-1 Additional Examples Simplify (2x3 + 4x2 – 6) – (5x3 + 2x – 2). Method 1: Subtract vertically. Line up like terms. Then add the coefficients. (2x3 + 4x2 – 6) Line up like terms. –(5x3 + 2x – 2) 2x3 + 4x2 – 6 Distribute the minus sign (in other words, add the –5x – 2x opposites) –3x3 + 4x2 – 2x – 4

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**Method 2: Subtract horizontally.**

Adding and Subtracting Polynomials LESSON 8-1 Additional Examples (continued) 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. = (2x3 – 5x3) + 4x2 – 2x + (–6 + 2) Group like terms. = –3x3 + 4x2 – 2x – 4 Simplify.

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**–2x2 + 3x – 4; quadratic trinomial**

Adding and Subtracting Polynomials LESSON 8-1 Lesson Quiz Write each expression in standard form. Then name each polynomial by its degree and number of terms. 1. –4 + 3x – 2x2 2. 2b2 – 4b3 + 6 3. (2x4 + 3x – 4) + (–3x x4) 4. (–3r + 4r2 – 3) – (4r2 + 6r – 2) –2x2 + 3x – 4; quadratic trinomial –4b3 + 2b2 + 6; cubic trinomial 3x4; fourth degree monomial –9r – 1; linear binomial

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