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Add or subtract 1. (x 2 + 4x – 1) + (5x 2 – 6x + 4) 2. (5y 2 – 9y + 1) – (7y 2 – 8y – 6) Find the product 3.(x – 6)(3x + 4) 4.(2x + 5)(3x + 4) 6x 2 – 2x + 3 -2y 2 – y + 7 3x 2 – 14x – 24 6x 2 + 23x + 20

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# of Terms Name by # of Terms 1 Monomial 2 Binomial 3 Trinomial 4+Polynomial

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Degree (largest exponent) Name by degree 0 Constant 1 Linear 2 Quadratic 3Cubic

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Identify the polynomial by degree and by the number of terms. Linear Binomial Degree: # of Terms: Leading Coefficient: 74

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Identify the polynomial by degree and by the number of terms. Cubic Monomial Degree: # of Terms:

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Identify the polynomial by degree and by the number of terms. Quadratic Trinomial Degree: # of Terms: Leading Coefficient: 5

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Multiplying Polynomials Binomial Theorem and Pascals Triangle

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1n = 0 1 1n = 1 1 2 1n = 2 1 3 3 1n = 3 ???n = 4

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Binomial Theorem 1n = 0 1 1n = 1 1 2 1n = 2 1 3 3 1n = 3 (a+b) 0 = 1 (a+b) 1 = 1a + 1b (a+b) 2 = 1a 2 + 2ab + 1b 2 (a+b) 3 = 1a 3 + 3a 2 b + 3ab 2 + 1b 3

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Binomial Theorem 1n = 0 1 1n = 1 1 2 1n = 2 1 3 3 1n = 3 Use the binomial theorem to write out (x + 3) 2.

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Binomial Theorem 1n = 0 1 1n = 1 1 2 1n = 2 1 3 3 1n = 3 Use the binomial theorem to write out (x + 3) 3.

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Binomial Theorem 1n = 0 1 1n = 1 1 2 1n = 2 1 3 3 1n = 3 Try (x + 2) 4.

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Application x + 2 Find an expression for the area of the base and then, the volume of the box: A = x 2 + 4x + 4 V = x 3 + 6x 2 + 12x + 8 x + 2

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Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x 2 - 53) -(x – 6) Simplify each expression. 4) (x + 5)

Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x 2 - 53) -(x – 6) Simplify each expression. 4) (x + 5)

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