Examine the expression 3x + 18. Find the greatest common factor. The GCF is 3.
Divide the terms within the expression by the greatest common factor: 3x ÷ 3 = x and 18 ÷ 3 = 6.
Write the GCF in front of a set of parentheses and write the remainders from the division process inside the parentheses. Because both terms are positive, use the addition property: 3(x + 6).
Redistribute to check your work: 3(x) + 3(6) = 3x + 18, which is the original expression.
Examine the expression 24x^2 + 8x - 2. Find the GCF, which is 2.
Divide the terms by the GCF, writing the GCF before the parentheses and the remainders inside the parentheses: 2(12x^2 + 4x - 1). Now you will factor the expression in the parentheses.
Break down the first and last terms, 12 and 1. With the last term, it is easy, only 1 x 1 = 1, but for the first term, 12 has several factors, 1, 12, 2, 6, 3 and 4. Look for the factors that when added or subtracted will equal the middle term, 4 from the expression. Only 6 and 2 satisfy this requirement.
Write the expression as a product of factors: 2(2x + 1)(6x - 1). Redistribute to check your work.
Examine the expression 7x^3 + 63x + 3x^2 + 27.
Divide the expression down the middle. This process is called grouping and leaves the expressions 7x^3 + 63x and 3x^2 + 27.
Examine the first group 7x^3 + 63x. Both terms have to common factors, 7 and x^2. (Remember that x^3 is actually x^2 times x.)
Divide the expression by the GCFs and write the remainders in parentheses: 7x(x^2 + 9).
Examine the second group 3x^2 + 27. Three is the only GCF.
Divide the expression by the GCF and write the remainders in parentheses: 3(x^2 + 9). If the parentheses from both groups match, you have factored correctly.
Write the terms outside of the parentheses together in a set of parentheses: (7x + 3).
Write the parenthetical terms next so that the outside and inside terms will create a product of factors: (7x + 3)(x^2 + 9).