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- Identify Quadratic Trinomial: Identify the quadratic trinomial and check if there is a common factor for all terms.Check for common factors:GCD(, , ) =
- Factor Out GCD: Factor out the greatest common divisor (GCD) from the quadratic trinomial.
- Find Two Numbers: Now, we need to factor the quadratic expression inside the parentheses. Look for two numbers that multiply to (the product of the coefficient of and the constant term) and add up to (the coefficient of ).The numbers that satisfy these conditions are and .
- Rewrite Middle Term: Rewrite the middle term using the two numbers found in the previous step.
- Group and Factor: Group the terms in pairs and factor by grouping.
- Factor Common Factors: Factor out the common factors from each group.
- Re-evaluate Factors: Notice that and are not common factors, and we cannot factor further. This indicates a mistake was made in the previous steps because the quadratic should be factorable. We need to re-evaluate the factors of that add up to .
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