Steps for Factoring Quadratic Equations

Steps for Factoring Quadratic Equations

1. 1. Identify the Terms

   • Look at all the terms in the expression and identify any common factors they may have. A common factor is a number or algebraic term that divides evenly into each term.
     • The terms are: 12x^3, -18x^2, and 6x
       • 3. Determine the Common Factors
         • Identify the factors that are common to all the terms. These are the factors that appear in each term. For example, if you have the terms 4x^2 and 8x, the common factor is 4x because it divides evenly into both terms.
           • Common factors: 1, x, 2, 3, 6
             • 5. Factor Out the GCF:
               • Once you have determined the GCF, factor it out from each term in the expression. This involves dividing each term by the GCF. For example, if the GCF is 4x and the expression is 4x^2 + 8x, factoring out the GCF yields 4x(x + 2).
                 • Divide each term by the GCF, which is 6x, and rewrite the expression. 12x^3 - 18x^2 + 6x = 6x(2x^2 - 3x + 1)

2. 12x^3 - 18x^2 +6x

3. 2. Find the Factors

   • For each term, determine all its factors. Factors are numbers or algebraic expressions that divide evenly into a given term without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
     • Factors of 12x^3: 1, 2, 3, 4, 6, x, x^2, x^3, 2x, 3x, 4x, 6x, 12x, 2x^2, 3x^2, 4x^2, 6x^2, 12x^2, x^3, 2x^3, 3x^3, 4x^3, 6x^3, 12x^3 Factors of -18x^2: 1, 2, 3, 6, x, x^2, 2x, 3x, 6x, 9x^2, 18x, x^2, 2x^2, 3x^2, 6x^2, 9x^2, 18x^2 Factors of 6x: 1, 2, 3, 6, x, 2x, 3x, 6x
       • 4. Determine the Greatest Common Factor
         • From the common factors you identified, determine the largest factor. This is the GCF. If there are no common factors, the GCF is 1.
           • In this case, the largest common factor is 6x.