Use either a tabular model or the distributive property to multiply (x-5)(6x^2-4x+3). 

Let's use the distributive property to multiply \((x - 5)(6x^2 - 4x + 3)\).

### Step 1: Distribute each term of the first polynomial
Distribute \(x\) across the terms in \(6x^2 - 4x + 3\):
\[
x \times 6x^2 = 6x^3
\]
\[
x \times -4x = -4x^2
\]
\[
x \times 3 = 3x
\]

So, \(x \times (6x^2 - 4x + 3)\) gives:
\[
6x^3 - 4x^2 + 3x
\]

### Step 2: Distribute \(-5\) across the terms in \(6x^2 - 4x + 3\)
\[
-5 \times 6x^2 = -30x^2
\]
\[
-5 \times -4x = 20x
\]
\[
-5 \times 3 = -15
\]

So, \(-5 \times (6x^2 - 4x + 3)\) gives:
\[
-30x^2 + 20x - 15
\]

### Step 3: Add the results from both distributions
Combine the like terms from the two results:
\[
6x^3 - 4x^2 + 3x - 30x^2 + 20x - 15
\]

Now, simplify by combining like terms:
\[
6x^3 + (-4x^2 - 30x^2) + (3x + 20x) - 15
\]
\[
6x^3 - 34x^2 + 23x - 15
\]

### Final Answer
The product is \(6x^3 - 34x^2 + 23x - 15\).

Would you like details or have any questions?

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**Related Questions:**
1. How do you use the tabular method to multiply polynomials?
2. What is the result of multiplying \((2x + 3)(3x^2 + 4x + 5)\)?
3. How do you expand and simplify \((x + 2)(x^2 - 3x + 4)\)?
4. How can you verify the result of a polynomial multiplication?
5. What are some common mistakes to avoid when using the distributive property?

**Tip:** When using the distributive property, be careful with signs, especially when distributing negative numbers.

Learn how to multiply polynomials (x-5)(6x^2-4x+3) using the distributive property with a detailed step-by-step solution. This problem covers polynomial multiplication concepts and the application of the distributive property. Suitable for students in Grades 9-12.

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