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Lesson 2.1 Adding and Subtracting Polynomials.

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Standard and EQ Standard MM1A2c: Add, subtract, multiply and divide polynomials. Essential Question- What is a polynomial and how do I add and subtract them?

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Vocabulary Monomial- a number, a variable, or the product of a number and one or more variables with whole number exponents. Examples: 12, x 2, 15x 4, 2a 3 b 4

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Vocabulary Degree of a Monomial- The sum of the exponents of the variables in the monomial. (The degree of a nonzero constant term is 0.) Example: x 2 has a degree of 2. 15x 4 has a degree of 4. 15x 4 has a degree of 4. 2a 3 b 4 has a degree of 7. 2a 3 b 4 has a degree of 7. 13 has a degree of 0. 13 has a degree of 0.

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Vocabulary Polynomial- a monomial or sum of monomials, each called a term of a polynomial. Example: 2x 4 +3x 2 -6 is a polynomial with 3 terms.

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Vocabulary Degree of a Polynomial- The greatest degree of its terms. Example: 2x 4 +3x 2 -6 has a degree of 4.

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Vocabulary Leading Coefficient- The coefficient of the first term of a polynomial when it is written in decreasing order from left to right. Example: 2x 4 +3x 2 -6 has a leading coefficient of 2.

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Vocabulary Binomial- A polynomial with two terms. Examples: 2x 4 +3x 2 3x 2 -6 3x 2 -6 Trinomial- A polynomial with three terms. Examples: 2x 4 +3x 2 -6 10 x 4 +5x 2 -13 10 x 4 +5x 2 -13 2x 4 +3x 2 -6 2x 4 +3x 2 -6

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Rewriting a Polynomial Write 12x 3 -15x+13x 5 so that the exponents decrease from left to right. Identify the degree and the leading coefficient. Degree is 5 13x 5 +12x 3 -15x 13x 5 +12x 3 -15x Leading coefficient is 13

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Rewriting Polynomials Rewrite the following so that exponents decrease from left to right. Identify the degree and leading coefficient. 9-2x 2 16+3y 3 +2y 6z 3 +7z 2 -3z 5 4ab+5a 2 b 2 -8a 2 b 4y+3xy+4

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Adding Polynomials Find the sum. (3x 4 -2x 3 +5x 2 )+(7x 2 +9x 3 -2x) Vertical format: Align like terms vertically. 3x 4 -2x 3 +5x 2 3x 4 -2x 3 +5x 2 + 9x 3 +7x 2 -2x + 9x 3 +7x 2 -2x 3x 4 +7x 3 +12x 2 -2x 3x 4 +7x 3 +12x 2 -2x Horizontal format: Group like terms and simplify (3x 4 -2x 3 +5x 2 )+(7x 2 +9x 3 -2x)=(3x 4 ) + (-2x 3 +9x 3 ) + (5x 2 +7x 2 ) + (-2x) = 3x 4 +7x 3 +12x 2 -2x

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Adding Polynomials Find the sum. (2a 2 + 7) + (7a 2 +4a-3) (9b 2 – b + 8) + (4b 2 – b – 3) (3z 2 + z – 4) + (2z 2 + 2z – 3) (8c 2 – 4c +1) + (-3c 2 + c + 5)

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Subtracting Polynomials Find the difference. (3x 2 – 9x) – (2x 2 – 5x + 6) Vertical format: 3x 2 – 9x 3x 2 – 9x 3x 2 – 9x 3x 2 – 9x - (2x 2 – 5x + 6)- 2x 2 + 5x – 6 YOU MUST x 2 – 4x – 6 DISTRIBUTE THE NEGATIVE SIGN!!!!!

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Subtracting Polynomials Find the difference. (3x 2 – 9x) – (2x 2 – 5x + 6) (3x 2 – 9x) – (2x 2 – 5x + 6) Horizontal format: DISTRIBUTE THE NEGATIVE SIGN!!! 3x 2 – 9x – 2x 2 + 5x – 6 Group like terms and simplify. (3x 2 -2x 2 ) + (-9x + 5x) + (-6) = x 2 – 4x – 6

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Subtracting Polynomials Find the difference (7c 3 – 6c + 4) – (9c 3 – 5c 2 – c) (d 2 – 15d +10) – (-12d 2 + 8d – 1) (-4m 2 + 3m – 1) – (m + 2) (3m + 4) – (2m 2 – 6m + 5)

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Adding Polynomials to Find Perimeter Write a polynomial that represents the perimeter of the figure. Perimeter is the sum of all sides. So, P= (2x+4) + (2x+4) + (x-5) + (3x+1) 3x+1 X-5 2x+4

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Vertical Method: 2x + 4 x – 5 x – 5 + 3x + 1 + 3x + 1 8x + 4 Horizontal Method: (2x+4) + (2x+4) + (x-5) + (3x+1) = (2x+2x+x+3x) + (4+4-5+1) = 8x + 4 = 8x + 4 Adding Polynomials to Find Perimeter

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