Factoring by Grouping
Factoring by grouping is a technique for factoring polynomials when no single factor is common to all terms. It is especially useful for four-term polynomials. The idea is to split the polynomial into smaller groups of terms, factor the GCF out of each group separately, and then extract the common binomial factor that emerges.
The procedure has four steps:
- Group terms with common factors. Separate the polynomial into two pairs of terms, choosing pairs that share a common factor.
- Factor out the common factor in each group. Apply GCF factoring within each pair independently.
- Factor the common factor from the expression. After factoring each group, a common binomial factor should appear in both groups — factor it out using the reverse Distributive Property.
- Check by multiplying the factors. Distribute to verify the product equals the original polynomial.
When the second group involves subtraction, take special care with signs while factoring out its GCF — factoring out a negative value reverses the signs inside the parentheses and is often necessary to produce a matching binomial in both groups.
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