factor the expression x^4+4x^3+6x^2+4x+1?

Answer 1

Notice that the constant is 1, so that if there are integer factors,
then they can only be 1 or -1. Because of all the plus signs in
the expression, you can rule out -1.
Now you need only try (x + 1) as a factor.

Dividing (x + 1) into the expression using synthetic division
gives the factor : x^3 + 3x^2 + 3x + 1.

This might work again, so now try synthetic division of
(x + 1) divided into x^3 + 3x^2 + 3x + 1.
You should get : x^2 + 2x + 1

And trying once more on this latter expression gives : x + 1

So, x^4 + 4x^3 + 6x^2 + 4x + 1 = (x + 1)^4

Answer 2

(x+1)^4

Answer 3

(X+1)^4

Answer 4

(X+1)^4