The problem asks you to find $(f \cdot g)(x)$ given two functions $f(x) = 3x - 10$ and $g(x) = 2x^2 - 4x + 3$.

The operation $(f \cdot g)(x)$ represents the product of the functions $f(x)$ and $g(x)$, which means:

$(f \cdot g)(x) = f(x) \cdot g(x)$

Substituting the given functions:

$(f \cdot g)(x) = (3x - 10) \cdot (2x^2 - 4x + 3)$

To multiply these expressions, distribute $3x - 10$ over each term in $2x^2 - 4x + 3$:

$(f \cdot g)(x) = 3x \cdot 2x^2 + 3x \cdot (-4x) + 3x \cdot 3 - 10 \cdot 2x^2 - 10 \cdot (-4x) - 10 \cdot 3$

Now, calculate each term:

$(f \cdot g)(x) = 6x^3 - 12x^2 + 9x - 20x^2 + 40x - 30$

Combine like terms:

$(f \cdot g)(x) = 6x^3 - 32x^2 + 49x - 30$

So the expression for $(f \cdot g)(x)$ in standard form is:

$(f \cdot g)(x) = 6x^3 - 32x^2 + 49x - 30$

Would you like any further details or have any questions?

Here are 5 related questions you might consider:

1. How do you differentiate the function $(f \cdot g)(x) = 6x^3 - 32x^2 + 49x - 30$?
2. What is the result of $f(x) + g(x)$ for the given functions?
3. How would you solve $(f \cdot g)(x) = 0$ for $x$?
4. Can you factor the expression $6x^3 - 32x^2 + 49x - 30$?
5. What is the domain of the function $(f \cdot g)(x)$?

Tip: Always check your final expression by re-expanding the factors to ensure the multiplication was done correctly.