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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Learning Goals: I can simplify polynomial expressions

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2x + 5 is an Algebraic Expression 2x and 5 are called the terms of the expression. 2x is a variable term 2 is the coefficient and x is the variable Unit 2: Algebra Lesson 1 – Introduction to Polynomials 5 is the constant

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Like Terms: Terms that have the same variable AND the same exponent. Unlike Terms: Terms that have the different variables OR different exponents

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Variable terms and constant terms (no variables, just numbers) can be put together through addition or subtraction to form polynomials.

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials There are 3 main types of polynomials: 1.Monomials – polynomials with only 1 term Ex. 3y 2, -w, 2xy

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials There are 3 main types of polynomials: 2.Binomials – polynomials with 2 unlike terms (put together by addition or subtraction) Ex. 6x - 2, 5x + 3y

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials There are 3 main types of polynomials: 3.Trinomials – polynomials with 3 unlike terms (put together by addition or subtraction) Ex. 5w 2 – 7w -1, 3xy + 2x - 5

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials If there are more than 3 unlike terms, we just call it a polynomial.

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Polynomials can be simplified by combining like terms. Steps for simplifying a polynomial: Identify the like terms Add or subtract the coefficients of the like terms Keep the variables the same

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Example: Simplify: 9a + 5 – 3a + 2 Step one: Identify the like terms: 9a + 5 – 3a + 2 *Note: Keep the sign to the left of the term with that term.*

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Example: Simplify: 9a + 5 – 3a + 2 Step two: Add or subtract the coefficients of the like terms: 9a – 3a + 2 + 5 9 – 3 = 6 2 + 5 = 7

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Example: Simplify: 9a + 5 – 3a + 2 Step three: Keep the variables the same: 9a – 3a + 2 + 5 9a – 3a = 6a 2 + 5 = 7 Answer: 6a + 7

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Example: Simplify the following expression: 3y 2 – y – 5y 2 + 6 3y 2 – 5y 2 = -2y 2 The other terms are all unlike so there is nothing we can do with them. Answer: -2y 2 – y + 6

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Example 3: Simplify the following expression: 2x 2 y + yx 2 – 0.4x 2 – 0.5x 2 y 2x 2 y + yx 2 -0.5x 2 y = 2.5x 2 y The other terms are all unlike so there is nothing we can do with them. Answer: 2.5x 2 y – 0.4x 2

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Example 4: Simplify the following expression: 4ab 2 + 12b 2 +ab 2 +0.2a 2 b+1.3a 2 b 4ab 2 + ab 2 = 5ab 2 0.2a 2 b + 1.3a 2 b = 1.5a 2 b The other terms are all unlike so there is nothing we can do with them. Answer: 5ab 2 + 1.5a 2 b + 12b 2

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Practice Read Page 256 “Key Ideas” Do Page 257 Q# 1, 2, 3, 4, 5

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