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).