To factor out the greatest common factor (GCF) from the polynomial \( 45t^5 - 15t^2 \), we first identify the GCF of the coefficients and the variables:
- The coefficients are 45 and -15. The GCF of 45 and 15 is 15.
- For the variable \( t \), the lowest power of \( t \) in the terms is \( t^2 \).
Thus, the GCF of the entire expression \( 45t^5 - 15t^2 \) is \( 15t^2 \).
Now we can factor it out:
\[ 45t^5 - 15t^2 = 15t^2(3t^3 - 1) \]
So, the factored expression is:
\[ 15t^2(3t^3 - 1) \]