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Using the preliminary factoring strategy, which method applies to p^2 + 5p + pq + 5q?
AGrouping, since it has more than three terms
BUndo FOIL, since it is a trinomial with leading coefficient 1
CFactor out a GCF, since every term shares a common factor
DThe difference of squares pattern, since it is a binomial
Answer & Solution
Correct answer: A. Grouping, since it has more than three terms
1. The expression p squared plus 5p plus pq plus 5q has four separate terms and no factor shared by all of them.
2. Since it is not a binomial or trinomial, the grouping method applies: it has more than three terms.
3. Undo FOIL only applies to trinomials, a GCF step requires a shared factor across all terms, and the difference of squares pattern needs a two-term binomial, so none of those fit here.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_
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