Fractions, also known as ratios, represent the incomplete division of two numbers. For example, 2/3 really means two divided by three. To many students, fractions can be annoying, especially when it comes to factoring polynomials. You can simplify the factoring process and remove any fractions by following a few basic steps. Once the fractions are gone, the rest of the math is pretty easy.
Determine the least common denominator, or LCD. Consider every denominator present in your polynomial. Then find the least number that each denominator can divide into without producing a remainder. For example, if you had 2/3 x + 1/5, then 15 would be the least common denominator since 15 is the first number both 3 and 5 divide into perfectly.
Factor out the LCD. For instance, if you had 1/3 x^2 + 1/2 x - 3/5, then you would factor out 1/30 as follows: 1/30 (10x^2 + 15x - 18). The remaining polynomial, 10x^2 + 15x - 18, is the result of distributing the LCD, 30, to the original polynomial.
If possible, finish factoring using other methods. In some instances, you will only be able to factor out the LCD. Otherwise, you can go further. For example, 1/2 x^2 - 2 becomes 1/2 (x^2 - 4), which can then be factored into 1/2 (x - 2) (x + 2) using the difference of squares method of factoring. Once you factor completely, you are done.
To factor out a fraction, multiply by the reciprocal. For instance, factoring 1/2 from 5x is equivalent to 1/2 (2 times 5x) which equals 1/2 (10x).