Question

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
45t^5–15t^2

Answer 1

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:

1. The coefficients are 45 and -15. The GCF of 45 and 15 is 15.
2. 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:

\[
15t^2(3t^3 - 1)
\]