Answer:
To factor completely using the GCMF (Greatest Common Monomial Factor), we first need to identify the common monomial factor of all three terms. In this case, the common monomial factor is 2x²:
10x^5 + 8x^4 - 4x² = 2x²(5x^3 + 4x^2 - 2)
Now, we can see that the expression can be factored further, but it cannot be factored using the GCMF. However, we can use other factoring techniques, such as grouping or factoring by grouping, to factor the remaining expression:
2x²(5x^3 + 4x^2 - 2) = 2x²(5x^3 + 10x^2 - 6x^2 - 2)
= 2x²(5x^2(x + 2) - 2(x + 2))
= 2x²(5x^2 - 2)(x + 2)
Therefore, the expression 10x^5 + 8x^4 - 4x² can be factored completely as 2x²(5x^2 - 2)(x + 2).
Explanation: