Algebra 1, The Box Method"/"The AC Method to factor

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Factoring means breaking down algebraic expressions into simpler parts that multiply together. For simple trinomials like x squared plus 5x plus 6, we can easily factor them into x plus 2 times x plus 3. However, when we encounter more complex trinomials like 2x squared plus 7x plus 3, where the leading coefficient is not 1, traditional factoring becomes difficult. For the general form ax squared plus bx plus c where a is not equal to 1, we need systematic approaches like the Box Method and AC Method. The AC Method is a systematic approach for factoring trinomials where the leading coefficient is not 1. Let's use the example 2x squared plus 7x plus 3. First, multiply a times c, which is 2 times 3 equals 6. Next, find two numbers that multiply to 6 and add to 7. These numbers are 6 and 1. Then split the middle term: 2x squared plus 6x plus 1x plus 3. Finally, factor by grouping: 2x times x plus 3, plus 1 times x plus 3, which gives us 2x plus 1 times x plus 3.