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Factorization Techniques for Quadratic Expressions in Mathematics

This guide covers essential factorization techniques for quadratic expressions, including finding the greatest common factor, utilizing the difference of squares, and factoring trinomials. It explores methods such as the Hoffman Method for expressions of the form ax² + bx + c and gives examples like 2x² + 3x and x² + 7x + 12. Understanding these concepts is crucial for solving quadratic equations and simplifying mathematical expressions. Homework exercises are included to reinforce learning, with specific problems designed to practice the techniques discussed.

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Factorization Techniques for Quadratic Expressions in Mathematics

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. Section 8c – Factorization of Quadratic Expressions Quadratic Expression

  3. Greatest Common Factor • 2x2 + 3x • (x – 5)2 – 2(x – 5) • (x + 2)2 + 2x + 4

  4. Difference of Squares • x2 – 9 • 25y6 – 49x2 • 2x2 – 8

  5. Difference of Squares Factor: • x2 – 11 • (x + 3)2 – 5 • (3x + 2)2 – 9

  6. DO NOT WRITE THIS DOWN. Factoring Trinomials Multiply Factor (x+ 3)(x + 4) x2 + 7x + 12 What if we started out with and wanted to get to

  7. Factoring Trinomials Factor: x2 + 7x + 12

  8. Section 8d – Factorization of ax2 + bx + c Factor • x2+ 8x + 12 • x2 + 4x – 21

  9. The Hoffman Method forfactoring ax2 + bx +c 6x2 + 7x – 3

  10. Factoring ax2 + bx +c • 3x2+ 5x + 2 • 15x2 + x – 6

  11. Factoring ax2 + bx +c • 5x2 – 13x + 6 • 12x2 – 1x – 6

  12. Factor completely • 3x2 – 9x + 6 • 6x2 – 20x – 16

  13. Homework • Pg 247-251 • C.1 – 1aei, 2adi • C.2 – 1afh, 2aef, 3aei, 4aeh • C.3 – 1adi, 2bef • C.4 – 1aeho, 2aeil • Pg 254 • 1aeil • 2aglru

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