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Factor the following four-term polynomial by grouping. 5x+20+xy+4y

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Final answer:

To factor the polynomial 5x+20+xy+4y by grouping, separate the terms into pairs and factor out the common factors in each pair. Then combine the factored terms to get the final result (x+4)(5+y).

Step-by-step explanation:

To factor the polynomial 5x+20+xy+4y by grouping, we can group the terms into pairs:

(5x+20) + (xy+4y)

To factor out the greatest common factors from each pair, we factor 5x+20 as 5(x+4) and factor xy+4y as y(x+4):

5(x+4) + y(x+4)

Now we can see that (x+4) is a common factor, so we can factor it out:

(x+4)(5+y)

Therefore, the factored form of the polynomial 5x+20+xy+4y is (x+4)(5+y).

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