Just following the property of rational number, rational function is also a ratio of two polynomial Functions. When we have two polynomial Functions and we want to get the ratio of two we get an equation in form of a Rational Function. We represent the rational function as:
f(x) = p(x) /q(x)
Here f(x) is a rational function and p(x) and q(x) are two polynomial function.
We are here to understand factoring rational functions:
Step 1: We have to find the greatest common factor of both numerator and denominator polynomial function. The greatest common factor is the polynomial function which is having the largest common term of all the term in both the functions.
Step 2: After finding the greatest common factor from the numerator polynomial function and from the denominator polynomial function. Divide the polynomial by the greatest common factor and then multiply with the rest term and we will get the resulting equation.
Step 3: We can also get the factors by guessing factors, by making group of factors, with Square formula, it all depend on type of polynomial function we have. We use the difference method when we have binomial function. We use grouping method when we have 4 terms or more. Just like this we apply different-different methods depending on the Polynomials.
Step 4: Just like methods we applied in numerator function, we apply in case of denominator function.
Step 5: If we get any factors in common we cancel those factors in numerator and denominator we make the rational function simple.