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How to Factor Binomials With Negative Exponents

A binomial is a mathematical expression that contains two terms. These terms can include numbers, called constants, and letters, called variables. A binomial is a type of polynomial. An exponent is a number that raises a term to a certain power, the result of multiplying the term by itself a given number of times. If you have negative exponents in a binomial expression, your expression is not in its simplest form. You can factor binomials to simplify them by following a few simple guidelines.

Instructions

- 1
  Write the number 1 followed by a fraction sign: /.
- 2
  Move the term or terms with negative exponents to the denominator (bottom position) of the fraction. For instance, you would factor x^-3 + x^-5 as 1/x^-3 + x^-5.
- 3
  Remove the negative signs from the exponents once you have shifted them to the denominator. In this example, you would write 1/x^3 + x^5.
- 4
  Combine like terms if possible. For example, if you had 2x^-4 + x^-4, you would create the fraction 1/2x^4 + x^4. Since both terms of the binomial are alike (some quantity of x^4), you can add them to get a factored answer of 1/3x^4.

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