The expression \( 8x^3 + 12x^2 - 6x + 1 \) is a polynomial of degree 3. Here are a few things you might want to do with this polynomial:

### Factoring
Factoring a cubic polynomial can be complex, and not all cubic polynomials can be factored into simpler polynomials with rational coefficients. For this particular polynomial, let's check if it can be factored by trying to find rational roots using the Rational Root Theorem.

The Rational Root Theorem states that any rational root, expressed in its lowest terms \( \frac{p}{q} \), is a factor of the constant term (here, 1) divided by a factor of the leading coefficient (here, 8).

The possible rational roots are \( \pm 1, \pm \frac{1}{2}, \pm \frac{1}{4}, \pm \frac{1}{8} \).

Let's test these possible roots:

1. \( x = 1 \):
\[
8(1)^3 + 12(1)^2 - 6(1) + 1 = 8 + 12 - 6 + 1 = 15 \neq 0
\]

2. \( x = -1 \):
\[
8(-1)^3 + 12(-1)^2 - 6(-1) + 1 = -8 + 12 + 6 + 1 = 11 \neq 0
\]

3. \( x = \frac{1}{2} \):
\[
8\left(\frac{1}{2}\right)^3 + 12\left(\frac{1}{2}\right)^2 - 6\left(\frac{1}{2}\right) + 1 = 8 \cdot \frac{1}{8} + 12 \cdot \frac{1}{4} - 6 \cdot \frac{1}{2} + 1 = 1 + 3 - 3 + 1 = 2 \neq 0
\]

4. \( x = -\frac{1}{2} \):
\[
8\left(-\frac{1}{2}\right)^3 + 12\left(-\frac{1}{2}\right)^2 - 6\left(-\frac{1}{2}\right) + 1 = 8 \cdot -\frac{1}{8} + 12 \cdot \frac{1}{4} + 6 \cdot \frac{1}{2} + 1 = -1 + 3 + 3 + 1 = 6 \neq 0
\]

Since none of these possible rational roots work, the polynomial does not have any rational roots. Therefore, it cannot be factored into polynomials with rational coefficients.

### Derivative
If you are interested in finding the derivative of the polynomial, you can use the power rule:

\[
f(x) = 8x^3 + 12x^2 - 6x + 1
\]

\[
f'(x) = \frac{d}{dx}(8x^3) + \frac{d}{dx}(12x^2) + \frac{d}{dx}(-6x) + \frac{d}{dx}(1)
\]

\[
f'(x) = 24x^2 + 24x - 6
\]

### Evaluation
If you want to evaluate the polynomial at a specific value of \( x \), simply substitute that value into the polynomial. For example, to evaluate at \( x = 2 \):

\[
8(2)^3 + 12(2)^2 - 6(2) + 1 = 8 \cdot 8 + 12 \cdot 4 - 6 \cdot 2 + 1 = 64 + 48 - 12 + 1 = 101
\]

If you have any specific questions or need further assistance with this polynomial, feel free to ask!