### October 17th 2021 archive

This week in precalc 11, I learned how to factor a polynomial, specifically when there is a fraction within it. Here are some examples of polynomials with fractions, that can be factored: To be able to factor these easily, there should be only integers with the variables. This means you must find a greatest common denominator (GCD), so all the terms have the same number at the bottom of the fraction. Then, the fraction can be removed as a greatest common factor (GCF), and the polynomial can be factored. Here are the above examples, with the steps to take to factor:

Remember, if there is a variable by itself without a number in front, there is always an invisible 1. Also, don’t forget that all numbers/variables are fractions, even if they aren’t shown that way at first. If a variable, like x, is not written as a fraction, it has a denominator of 1.  You can also verify your answer when you are done, to check if it is correct. To do this, just take the final answer and use the distributive property with FOIL to get back to the polynomial you started with.