Factor completely. If the given polynomial is not factorable, indicate so by writing prime.
4x^3+8xy^2
2x(x^2 + 2y^2)
Well that's what I did and when I submit the answer it says that it is not correct.
4x^3+8xy^2
2x(2x^2+4y^2)
To factor the given polynomial 4x^3 + 8xy^2 completely, we first look for the greatest common factor (GCF) of all terms. In this case, the GCF is 4.
Factoring out the GCF of 4 gives us:
4(x^3 + 2xy^2)
Now, let's examine the remaining expression within the parentheses, x^3 + 2xy^2.
This expression has a common factor of x, so we can factor it further:
x(x^2 + 2y^2)
At this point, the expression x^2 + 2y^2 cannot be factored any further since it is a sum of squares.
Therefore, the completely factored form of the polynomial 4x^3 + 8xy^2 is:
4x(x^2 + 2y^2)
Note: This expression is not prime as it has two factors: 4x and (x^2 + 2y^2).