Question

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
36f9+36f5–12f2

Answer 1

To factor out the greatest common factor (GCF) from the polynomial \(36f^9 + 36f^5 - 12f^2\), we first need to determine the GCF of the coefficients and the variable parts.

1. **Coefficients**: The coefficients are 36, 36, and -12.
- The GCF of 36 and -12 is 12.

2. **Variable part**: The terms have \(f^9\), \(f^5\), and \(f^2\).
- The GCF for the variable parts is \(f^2\) (the lowest power of \(f\)).

Combining these, the overall GCF of the polynomial is \(12f^2\).

Now, we can factor out the GCF:

\[
36f^9 + 36f^5 - 12f^2 = 12f^2(3f^7 + 3f^3 - 1).
\]

So, the factored form of the polynomial is:

\[
12f^2(3f^7 + 3f^3 - 1).
\]