How to Factor Trinomials With Fractions

Use factoring and the reverse FOIL methods to solve trinomials.
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Trinomials are groups of three terms, usually in a form similar to x^2 + x + 1. To factor a normal trinomial, you either factor into two parts or look for the greatest common factor. When dealing with fractions, you will more than likely be looking for both. A trinomial involving fractions means you have trinomials divided by other trinomials, binomials or single terms. Once you grasp the method, factoring trinomials with fractions is no harder than factoring a regular trinomial.

    Write the entire problem and then break it into separate pieces. For instance, if you have one trinomial divided by another trinomial, then write the two trinomials again separately.

    Factor each polynomial as much as possible. Look for the greatest common factor (GCF), and also factor into separate groups, if possible. Grouping may also be an option. Regardless of which methods you use, factor completely before continuing.

    Write your problem again, but place the factored pieces in place of their original counterparts.

    Look for pieces that may cancel out the others. When canceling factors, the rules are as follows: The factors must be exactly the same. You can cancel out a factor only once. Factors can cancel only between numerators and denominators. You can cancel within the same fraction and between fractions. If trinomial fractions are being divided, you must invert the second fraction. This will turn the problem into a multiplication problem, allowing cancellation to occur.

    Multiply the remaining numerators and denominators.

    Factor the result, if possible.

    Tips

    • Factor each portion of each fraction before you try to cancel anything out. Double-check your work with each portion to ensure your factors are correct.

    Warnings

    • Always invert the second fraction if there is a division sign between fractions; otherwise, your solution will be incorrect. Never cancel out factors straight across. It must be top to bottom.

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