Factor the expression: 15x2n + 9xⁿ+1 - 3xⁿ.

The given expression is $15x^{2n} + 9x^{n+1} - 3x^n$.
First, find the GCF of the numerical coefficients: 15, 9, and 3. The greatest common divisor of these numbers is 3.
Next, find the GCF of the variable terms: $x^{2n}$, $x^{n+1}$, and $x^n$. The lowest power of $x$ present in all terms is $x^n$.
So, the GCF of the entire expression is $3x^n$.

Divide each term by $3x^n$:
For the first term, $\frac{15x^{2n}}{3x^n} = 5x^{2n-n} = 5x^n$.
For the second term, $\frac{9x^{n+1}}{3x^n} = 3x^{(n+1)-n} = 3x^1 = 3x$.
For the third term, $\frac{-3x^n}{3x^n} = -1$.