Question

actor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
22n10+11n5+11n4–11n2

Answer 1

To factor out the greatest common factor (GCF) from the polynomial \(22n^{10} + 11n^5 + 11n^4 - 11n^2\), let's first identify the GCF of the coefficients and the variable terms.

1. The coefficients are 22, 11, 11, and -11. The GCF of these numbers is 11.
2. The variable terms have \(n^{10}\), \(n^5\), \(n^4\), and \(n^2\). The lowest power of \(n\) is \(n^2\).

Therefore, the GCF of the entire polynomial is \(11n^2\).

Now, we can factor out \(11n^2\):

\[
22n^{10} + 11n^5 + 11n^4 - 11n^2 = 11n^2(2n^8 + n^3 + n^2 - 1)
\]

So, the factored form of the polynomial is:

\[
\boxed{11n^2(2n^8 + n^3 + n^2 - 1)}
\]