Write down a mathematical expression to factor. Use the binomial mathematical expression "6x^2 + 2x" for this example.
Breakdown the two terms of the expression so the individual terms are expressed as a multiple of all the factors in the term (except the number 1). Write down the new expression for this example as "2*3*x*x + 2*x", since 6 can be expressed as 2*3(2 times 3 equals 6) and x^2 is equal to x*x.
Identify the common factors in this expression as "x" and "2" since both "x" and "2" are in both terms of the expression. Identify that the Greatest Common Factor is the product of 2 times x, since the greatest common factor is defined as the product of the common factors in two or more terms.
Remove the greatest common factor from each of the terms of the original expression. Write a new expression such that it is the product of the greatest common factor and the expression from which the terms were removed. Use parenthesis to indicate that the greatest common factor is multiplied by the expression from which the terms were removed. Rewrite the new factored binomial expression for this example as 2x(3x + 1) since "2x" is the greatest common factor and "3x + 1" is the original expression with the greatest common factor, "2x", removed from each term.
Verify that the factored binomial expression is equal to the original expression. Multiply the expression outside the parenthesis (the greatest common factor) with the terms inside the expression using the distributive property. Multiply 2*x time 3*x to obtain 6x*2 and multiply 2x times 1 to obtain 2x and add the result to obtain "6x^2 + 2x"; the original binomial.
Check the results with an online binomial calculator like the one at the "Algebra.Help; Expression Factoring Calculator" page listed in the resources section below. Type the function 6x^2 + 2x into the function or equation box in the binomial calculator to see the steps, explanation and solution.