What is the product of (3x - 6) and (2x^2 - 7x + 1)?

1. Distribute the first term of the first binomial: Multiply $3x$ by each term in the second polynomial $(2x^2 - 7x + 1)$.
$3x \times 2x^2 = 6x^3$
$3x \times (-7x) = -21x^2$
$3x \times 1 = 3x$
So, $3x(2x^2 - 7x + 1) = 6x^3 - 21x^2 + 3x$.

2. Distribute the second term of the first binomial: Multiply $-6$ by each term in the second polynomial $(2x^2 - 7x + 1)$.
$-6 \times 2x^2 = -12x^2$
$-6 \times (-7x) = 42x$
$-6 \times 1 = -6$
So, $-6(2x^2 - 7x + 1) = -12x^2 + 42x - 6$.

3. Combine the results from both distributions: Add the expressions obtained in step 1 and step 2.
$(6x^3 - 21x^2 + 3x) + (-12x^2 + 42x - 6)$

4. Group like terms: Combine terms with the same power of $x$.
$6x^3 + (-21x^2 - 12x^2) + (3x + 42x) - 6$

5. Simplify by combining like terms: Perform the addition and subtraction for each group.
$6x^3 + (-33x^2) + (45x) - 6$
$6x^3 - 33x^2 + 45x - 6$