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Mastering Complex Base Factoring Techniques | Factor Polynomial Equations Easily

Learn and practice factoring polynomials with complex bases using regrouping, GCF, binomial, and trinomial techniques step by step. Enhance your factorization skills with examples and exercises to simplify expressions effectively.

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Mastering Complex Base Factoring Techniques | Factor Polynomial Equations Easily

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  1. Aim: How do we factor complex base and using regrouping Do Now: Factor the following 1. 5x2y – 10xy2 2. x2 – 5x + 6 3. x(y – 1) + 3(y – 1)

  2. The GCF can be a monomial or a binomial x(y – 1) + 3(y – 1) The GCF is y – 1 Factor y– 1, then write the remaining in another parenthesis = (y – 1)(x + 3) x2(y + 2) – (y + 2) = (y + 2)(x2 – 1) Factor y+ 2 = (y + 2)(x – 1)(x + 1) Factor (x2 – 1) again

  3. Factor: 2(5x + 2)2 – 7(5x + 2) Factor the GCF (5x + 2) =(5x + 2)[2(5x + 2) – 7] Simplify the expression in the bracket =(5x + 2)(10x + 4 – 7) =(5x + 2)(10x – 3)

  4. Factoring Expressions With Complex Bases (a + 2)2 + 3(a + 2) + 2 Let A = (a + 2). A2 + 3A + 2 Replace (a + 2) with A. = (A + 2)(A + 1) Factor the trinomial. = [(a + 2) + 2] [(a + 2) + 1] Replace (a + 2) with A. = (a + 4)(a + 3) Simplify.

  5. Factor by grouping Group into two binomials Factor by GFC if possible Factor by GFC Factor completely

  6. You Try It Factor each trinomial if possible. • 1)y(x – 2) + 3(x– 2) • 2) x2– x– xy+ y • 3) 5(2x – 3)2 + 9(2x – 3) • 4) (x – 3)2 – 6(x – 3) + 8 • 5) x3 + 3x2 – x – 3

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