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When factoring a trinomial like x^2 + 5x + 6, why does listing every factor pair of the constant term alongside its sum help?
AIt shows which pair divides evenly into the leading coefficient
BIt shows which pair is closest to the value of the trinomial
CIt shows which pair has the same sign as the leading term
DIt shows which pair multiplies to c and also adds to b
Answer & Solution
Correct answer: D. It shows which pair multiplies to c and also adds to b
1. The two numbers used as the last terms of the binomial factors must multiply to c and add to b at the same time.
2. Listing every factor pair of c next to its sum lets you scan for the one pair that also matches b.
3. The leading coefficient and the overall size of the trinomial play no role in this particular table, since this method is for trinomials with leading coefficient 1.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.2 Factor Quadratic Trinomials with Leading Coefficient 1_
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