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Polynomials and Factoring Review By: Ms. Williams

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Classifying Polynomials 1. Find the degree of the polynomial and name it based on its degree and number of terms. 2x + 5

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Answer Degree: 1 Name: Linear Binomial

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Adding and Subtracting Polynomials 1. Simplify the expression. (a 3 – 2a 2 ) + (3a 3 – 4a 2 )

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Answer 4a 3 – 6a 2

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Multiplying a Monomial and Trinomial 1. Simplify the expression. 3x 3 (x 2 + 5x – 8)

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Answer 3x 5 + 15x 4 – 24x 3

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Finding the GCF 1. Find the GCF of the polynomial. 18x 6 + 12x 3

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Answer 6x 3

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Factoring out the GCF 1. Factor out the GCF of the polynomial. 9x 4 + 6x 3 – 18x 2

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Answer 3x 2 (3x 2 + 2x – 6)

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Multiplying Binomials 1. Simplify the product. (x – 10)(x + 1)

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Answer x 2 – 9x – 10

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Multiplying a Binomial and Trinomial 1. Simplify the product. (x – 4)(x 2 + 2x – 9)

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Answer x 3 – 2x 2 – 17x + 36

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The Square of a Binomial 1. Simplify the product. (x – 12) 2

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Answer x 2 – 24x + 144

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The Difference of Squares 1. Simplify the product. (2x + 5)(2x – 5)

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Answer 4x 2 – 25

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Classifying Polynomials 1. Find the degree of the polynomial and name it based on its degree and number of terms. 3x 3 + 2x 2 – 1

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Answer Degree: 3 Name: Cubic Trinomial

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Adding or Subtracting Polynomials 1. Simplify the expression. (–4k 4 + 3k 2 + 14) – (4k 4 + 7k 2 – 6)

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Answer –8k 4 – 4k 2 + 20

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Multiplying a Monomial and Trinomial 1. Simplify the expression. (–6y 4 )(–5y 2 + 11y – 8)

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Answer 30y 6 – 66y 5 + 48y 4

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Finding the GCF 1. Find the GCF of the polynomial. 21x 2 y 5 + 35x 6 y

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Answer 7x 2 y

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Factoring out the GCF 1. Factor out the GCF of the polynomial. 27x 3 – 9x 2 + 18

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Answer 9(3x 3 – x 2 + 2)

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Multiplying Binomials 1. Simplify the product. (2x 2 + 7x)(9 – x)

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Answer –2x 3 + 11x 2 + 63x

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Multiplying a Binomial and Trinomial 1. Simplify the product. (3x 2 – 4x + 2)(2x + 3)

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Answer 6x 3 + x 2 – 8x + 6

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The Square of a Binomial 1. Simplify the product. (5x + 4) 2

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Answer 25x 2 + 40x + 16

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The Difference of Square 1. Simplify the product. (9x 2 + 10)(9x 2 – 10)

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Answer 81x 4 – 100

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Classifying Polynomials 1. Find the degree of the polynomial and name it based on its degree and number of terms. 45

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Answer Degree: 0 Name: Constant Monomial

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Adding and Subtracting Polynomials 1. Simplify the expression. (–x 4 + 13x 5 + 6x 3 ) + (6x 3 + 5x 5 – 7x 4 )

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Answer 18x 5 – 8x 4 + 12x 3

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Multiplying a Monomial and Trinomial 1. Simplify the product. 8m 7 (5m 3 – 7m 2 – 9)

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Answer 40m 10 – 56m 9 – 72m 7

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Finding the GCF 1. Find the GCF of the polynomial. –12x 4 – 60x 2 – 36x

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Answer 12x OR –12x

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Factoring out the GCF 1. Factor out the GCF of the polynomial. –12x 4 – 60x 2 – 36x

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Answer 12x(–x 3 – 5x – 3) OR –12x(x 3 + 5x + 3)

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Multiplying Binomials 1. Simplify the product. (x – 15)(x + 4)

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Answer x 2 – 11x – 60

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Multiplying a Binomial and Trinomial 1. Simplify the product. (x 2 – 6 – 2x)(6x + 1)

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Answer 6x 3 – 11x 2 – 38x – 6

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The Square of a Binomial 1. Simplify the product. (4x – 3y) 2

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Answer 16x 2 – 24xy + 9y 2

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The Difference of Squares 1. Simplify the product. (13a + 5b)(13a – 5b)

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Answer 169a 2 – 25b 2

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