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Understanding Factoring Quadratic Trinomials Using the FOIL Method

This resource covers the essential process of factoring quadratic trinomials, emphasizing the FOIL method through practical examples. It shows how to multiply binomials such as (7x + 3)(2x + 4) step-by-step, demonstrating the combination of the first, outer, inner, and last terms to arrive at the expanded form. By converting a trinomial like x² + 3x + 2 back into its binomial factors, learners will grasp the relationship between standard form and its factors. This guide reinforces understanding of standard form as ax² + bx + c and the conditions for successful factoring.

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Understanding Factoring Quadratic Trinomials Using the FOIL Method

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  1. Factoring Quadratic Trinomialsa = 1 Chapter 10.5

  2. RECALL: FOIL Example: Multiply using the FOIL method. (7x + 3)(2x + 4) O F (7x + 3)(2x + 4) I L F O I L = (7x)(2x) + (7x)(4) + (3)(2x) + (3)(4) = 14x2 + 28x+ 6x + 12 = 14x2 + 34x + 12

  3. Factoring Quadratic Trinomials • Factoring is “undoing” FOIL. • Starting with an expression like • x2 + 3x + 2 • We’re going to rewrite this as the product of 2 binomials. X + 2 ( )( ) X + 1

  4. Standard Form: ax2 + bx + c • The Standard Form of any Quadratic Trinomials is ax2 + bx + c So for the example, 3x2 − 4x + 1 a = 3 b = −4 c = 1

  5. Standard Form: ax2 + bx + c • EX. Find a, b and c • 4x2 + x − 2 • 2x2 − x + 5 • − x2 + 2x − 4 • x2 + 3x + 2

  6. Factoring: ax2 + bx + c when a = 1 Find the two numbers whose product equals c AND whose sum equals b

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