How to Use the AC Method for Factoring

You can find factoring problems in most algebra textbooks.
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Factoring is a mathematical process by which you break up a math phrase into simplified parts. This is a task that you probably will have to perform in a high school or college algebra course. There are multiple ways of factoring. One such method is known as the "AC" method, which uses the variables A, B and C as part of the factoring process.

    Correlate the letters A, B and C with the numbers in your equation. For example if you have 4x^2 + 9x + 5, you would match A with 4, B with 9 and C with the number 5.

    Multiply A by C. In this example, you would multiply 4 by 5 to get 20.

    List the factors of your answer from step two. That is, list pairs of numbers that you could multiply to come up with that answer. For instance, in the case of 20, you would have the following factors: (1, 20), (2, 10), (4, 5).

    Find a pair of numbers among the factors that adds up to the B term in the equation. For this example, you must find a pair that adds up to 9. Therefore, you would isolate the pair (4, 5).

    Replace the middle term (the B term) with the two numbers from the pair, along with the original variable that went with the B term. For example, you would write: 4x^2 + (4+5)x + 5 = 4x^2 + 4x + 5x + 5.

    Group the first two terms and the last two terms together as such: (4x^2 + 4x) + (5x + 5).

    Simplify the equation by finding terms that are common for each side. For instance, you would simplify (4x^2 + 4x) + (5x + 5) to 4x(x + 1) + 5 (x + 1). This would further simplify to (4x + 5) (x + 1).

    Tips

    • Make sure to write your equation in descending power. For example, 4x^2 + 9x + 5, not 9x + 4x^2 + 5. If A or C are negative, you must consider that when you factor. For instance, if A times C is -20 the factors are (-1, 20), (1, -20), (-2, 10), (2, -10), (-4, 5) and (4, -5).

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