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Warm-Up Factor the following expressions by pulling out things that each term has in common: 1.4x 3 + 8x 2 + 12xz 2.9x 2 y 3 + 3xy 2 + 27xy 4

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X-box Factoring

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Standard Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Objective: We will use the x-box method to factor trinomials.

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Factor the x-box way We are going to factor trinomials like 3x 2 + 27x + 60 using the X-Box method. Step 1: Write the polynomial in standard form. Step 2: Factor all common factors in the trinomial. Step 3: Use the X method. Step 4: Write your answer. Step 5: Check your answer by distributing

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Factor the x-box way Middle b=m+n Sum Product ac=mn m n First and Last Coefficients y = ax 2 + bx + c

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Examples Factor using the x-box method. 1. x 2 + 4x – 12 -12 4 6 -2 Solution: x 2 + 4x – 12 = (x + 6)(x - 2)

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Examples continued 2. x 2 - 9x + 20 20 -9 Solution: x 2 - 9x + 20 = (x - 4)(x - 5 ) -4 -5

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You try… Factor: x 2 – 6x + 5 Answer: (x – 1)(x – 5)

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Extra Practice Factor 1. x 2 + 6x + 5 (x + 5)(x + 1) 2. r 2 – 12r + 35 (r – 5)(r – 7)

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