Things You'll Need:
- Calculator
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Step 1
Decide if there is a greatest common factor that you can factor out of the problem. In 4x^3 - 36x^2 - 40x, you can factor out 4x to give you 4x(x^2 - 9x - 10).
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Step 2
Notice if there is a coefficient in front of the x^2 term after you factored out the greatest common factor. If there is not, list all of the possible factors of the last term. In this example, the possible factors of -10 are -1 * 10, 1 * -10, -2 * 5, 2 * -5.
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Step 3
Find the pair of factors that will add together to give you the coefficient of the middle term. The pair you want is 1 * -10.
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Step 4
Plug these factors into this pattern: (x +/- __)(x +/- __), leaving the factor you factored out in front. This looks like 4x(x + 1)(x - 10). This is the answer.
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Step 5
Factor by trial and error if there is a coefficient in front of the x^2 term. If you need to factor 6x^2 - 11x - 10, there is no common factor, so you must use trial and error.
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Step 6
List all of the factors of the coefficient of the first term and the last term. The factors of 6 are 1 * 6 and 2 * 3. The factors of -10 are -1 * 10, 1 * -10, -2 * 5, 2 * -5. Use your calculator to help you find these factors if needed.
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Step 7
Plug factors into this pattern: (__x +/- __)(__x +/- __). You could use 1 * 6 and -1 * 10, which would look like (1x - 1)(6x + 10).
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Step 8
Use the FOIL Method to check if you have the right combination. The FOIL Method requires you to multiply the First, Outer, Inner, and Last terms together and then combine like terms. In the first combination, (1x - 1)(6x + 10), 1x and 6x are the first terms, 1x and 10 are the outer terms, -1 and 6x are the inner terms, and -1 and 10 are the last terms. This gives you 6x^2 + 4x - 10, which is not correct because it is not the original trinomial.
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Step 9
Continue this trial and error method until you find the correct combination. For this example, (3x + 2)(2x - 5) gives you 6x^2 - 11x - 10, which is the original trinomial. This is your answer.
