Question

Factor x^4 + xy^3 + x^3 + y^3. Hint, first factor a monomial. Please explain why!!!

Answer 1

Pull an x from the first two terms

x(x^3 + y^3) + (x^3 + y^3)   Now x^3 + y^3 is a common factor.

(x^3 + y^3)*(x + 1) That should be far enough. It can be factored further by factoring (x^3 + y^3) but there is no point because you can't do anything after that. But in case you want to know how x^3 + y^3 factors

(x^3 + y^3) = (x + y)(x^2 - xy + y^2)

Which means you could write original polynomial as

(x + y)(x^2 - xy + y^2)(x + 1)

Part B

You factored the x out of xy^3 so that you would have a common factor (x^3 + y^3) to pull out as a common factor for the whole polynomial.