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Mastering Factoring: Quadratic Expressions and Greatest Common Factor (GCF)

This educational guide focuses on factoring quadratic expressions, emphasizing the process of identifying and factoring out the Greatest Common Factor (GCF). You'll learn to recognize and factor differences of squares, as well as the steps to factor quadratics in the form of ( ax^2 + bx - c ). The guide includes clear definitions, examples, and practice problems to enhance your understanding. Perfect for students seeking to improve their algebraic skills, this resource simplifies complex concepts into manageable steps.

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Mastering Factoring: Quadratic Expressions and Greatest Common Factor (GCF)

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  1. 5-4 Factoring Quadratic Expressions Objectives: Factor a difference of squares. Factor quadratics in the form Factor out the GCF. Factor quadratics with a GCF.

  2. Definitions Greatest Common Factor – the biggest number that will divide all terms evenly. If there are variables, the lower exponent is in the GCF. examples: Find the GCF 1) 9, 12

  3. Class Work 5-4 Find the GCF: 1) 18, 20 2) 12, 24, 30 3) 4x, 20x 4) x2, 6x 5) 27x2, 36 6) 5x2, 6xy 7) 3y, 8x 8) 2x3, 3x2 9) 36a4, 72a2

  4. Factor out the GCF 1) x2 – 9x 2) 3x2 – 18x 3) 12x3 – 18x2 4) 2x2 + 4x + 10

  5. Recognizing a Difference of Squares There are ONLY two terms in the problem. It MUST be a minus sign in the middle. BOTH terms are perfect squares This is an example of a difference of squares 4x2 - 25

  6. Perfect Squares 9 is a perfect square because 3 x 3 = 9 36 is a perfect square because 6 x 6 = 36 81 is a perfect square because 9 x 9 = 81 12 is NOT a perfect square because there is no number times itself that will give you 12.

  7. Circle the Perfect Squares 16, 36, 20, 121, 144, 60, 50, 4, 225 9x2, 10x2, 81x3, 100x2, 44x2, 1000x4, 30x2

  8. Class Work 5-4Factor: 1) x2 – 4 2) x2 - 81 3) 4x2 – x 4) 25x2 – 9 5) 100x4 – 49 6) 49x2 + 1 8) 4x2 + 25 9) 121x2 – 81y2

  9. Factoring Polynomials in the Formax2 + bx - c Factor: 1) x2 – 14x – 32 2) x2 + 13x + 22 3) x2 + 15xy + 14y2 4) x2 + 7x – 12 5) 6x2 + 13x + 2 6) 10x2 – 13x + 4

  10. Factoring Problems with a GCF 1) 4x2 – 16x – 48 2) 6x2 – 42x + 36 3) 2x2 + 46x – 100 4) x3 – 4x 5) 6x2 + 13x + 2 6) 6x2 – 6x - 72

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