alleryStart learning →Factor by grouping: xy + 3y + 2x + 6.
A(x+2)(y+3)
B(x+3)(y+2)
C(x+6)(y+1)
D(x+1)(y+6)
Answer & Solution
Correct answer: B. (x+3)(y+2)
1. Group the four terms into two pairs with a common factor in each: (xy + 3y) and (2x + 6).
2. Factor y from the first pair to get y(x + 3), and factor 2 from the second pair to get 2(x + 3).
3. Both pairs now share the common binomial factor (x + 3).
4. Factor out (x + 3) to get (x + 3)(y + 2), and check by multiplying: xy + 2x + 3y + 6 matches the original terms.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_
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