Question

Using the 4 train car strategy for factoring polynomials, what is the green common factor for the 1st two train cars and the green common factor for the 3rd and 4th train car: . note: the answers are intermediary steps. do not enter the final step or factored form, but this question is asking what is the intermediate step as the answer.
2x^2 + 4x + 3xy + 6y

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Answer 1

The completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)

How to factor the polynomial?

The expression is given as:

2x^2 + 4x + 3xy + 6y

Group the expression into two

[2x^2 + 4x] + [3xy + 6y]

Factor out each group

2x(x + 2) + 3y(x + 2)

Factor out x + 2

(2x + 3y)(x + 2)

Hence, the completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)

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