To factor out the greatest common factor from the polynomial \( 10c^3 - 4c^2 \), we need to identify the common factors in each term.
The coefficients are 10 and -4. The greatest common factor (GCF) of 10 and 4 is 2.
Next, we look at the variable parts. The terms are \( c^3 \) and \( c^2 \). The greatest common factor of \( c^3 \) and \( c^2 \) is \( c^2 \).
Now, we can factor out the GCF, which is \( 2c^2 \):
\[ 10c^3 - 4c^2 = 2c^2(5c - 2) \]
Thus, the factored form of the polynomial is:
\[ 2c^2(5c - 2) \]