Writing each expression in factored form. (Polynomials)

Question

I know how to factor polynomials, it’s just when it ask me to “write each expression in factored form” I get confused. Because when you factor a polynomial you get that factored equation so wouldn’t you just do the opposite and solve the equation?

ex. “Write expression in factored form”

x(y+1) + 4(y+1)

1. what my answer is*

= (xy + 1x) + (4y + 4)

1. the answer in answer key*

= (y + 1)(x + 4)

Answer 1

For the example you gave, the (y+1) is a common binomial factor.

Imagine instead the problem was:

xU + 4U

Now U is a common factor so you can rewrite as:

U(x+4).

But instead of factoring out a U in the original problem you are factoring out a binomial (y+1).

(y+1) (x+4)