Sure, let's proceed to solve the given problem:
Given algebraic expression:
14m^8 + 14m^7 - 42m^4
We are asked to factor out the greatest common polynomial from the given expression.
1. First, we look for a common factor. In all three terms of the given expression, '14' is common, as well as a power of 'm'.
2. The common factor is, therefore, '14m^4'. This is because among the powers of 'm' present in the given expression, 'm^4' is the smallest power.
3. Next, we divide each term by the greatest common polynomial '14m^4'.
Therefore,
14m^8/14m^4 + 14m^7/14m^4 - 42m^4/14m^4
becomes
m^4 + m^3 - 3
then, we place back the greatest common polynomial '14m^4' in the reflected expression.
4. Final factorized expression looks like this:
14m^4(m^4 + m^3 - 3)
So the factorized version of the given expression 14m^8 + 14m^7 - 42m^4 is 14m^4(m^4 + m^3 - 3).
This is the answer.