Example

Factoring 6pq2−9pq−6p6pq^2 - 9pq - 6p

Factor 6pq2−9pq−6p6pq^2 - 9pq - 6p completely.

Step 1 — Check for a GCF: The three terms share a greatest common factor of 3p3p. Factor it out: 3p(2q2−3q−2)3p(2q^2 - 3q - 2)

Step 2 — Factor the trinomial: The expression inside the parentheses is a trinomial with a leading coefficient other than 11 (a≠1a \neq 1). Factor it using the trial and error or "ac" method. The binomial factors are (2q+1)(2q + 1) and (q−2)(q - 2): 3p(2q+1)(q−2)3p(2q + 1)(q - 2)

Step 3 — Check: Verify by multiplying: 3p(2q+1)(q−2)=3p(2q2−4q+q−2)=3p(2q2−3q−2)=6pq2−9pq−6p3p(2q + 1)(q - 2) = 3p(2q^2 - 4q + q - 2) = 3p(2q^2 - 3q - 2) = 6pq^2 - 9pq - 6p ✓

The completely factored form is 3p(2q+1)(q−2)3p(2q + 1)(q - 2).

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Updated 2026-06-03

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