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The problem asks to rewrite the polynomial in standard form and to state its degree and constant term. Let's solve the part **b** of the question for the given polynomial:

\[ g(x) = 3(x+1)(x+3)(x-4) \]

### Step 1: Expand the polynomial

First, expand \((x+1)(x+3)\):
\[
(x+1)(x+3) = x^2 + 3x + x + 3 = x^2 + 4x + 3
\]

Now, multiply this by \((x-4)\):
\[
(x^2 + 4x + 3)(x-4) = x^2(x-4) + 4x(x-4) + 3(x-4)
\]
\[
= x^3 - 4x^2 + 4x^2 - 16x + 3x - 12
\]
\[
= x^3 - 13x - 12
\]

### Step 2: Multiply by the constant 3
Now, multiply everything by 3:
\[
g(x) = 3(x^3 - 13x - 12) = 3x^3 - 39x - 36
\]

### Final Result:
The polynomial in standard form is:
\[
g(x) = 3x^3 - 39x - 36
\]

### Degree and Constant Term:
- **Degree**: The highest power of \(x\) is 3, so the degree of the polynomial is 3.
- **Constant Term**: The constant term is \(-36\).

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Would you like further clarification or have any other questions?

Here are five related questions for further practice:
1. How would you expand a polynomial with four terms in the product?
2. What is the leading coefficient of \(g(x)\)?
3. Can you factor the expanded form back into its factored form?
4. What happens to the degree of a polynomial when multiplied by a constant?
5. How do you determine the constant term when given a factored form?

**Tip**: Always check the expanded terms carefully for any sign errors when multiplying polynomials!

Rewrite the polynomial g(x) = 3(x+1)(x+3)(x-4) in standard form, and state its degree and constant term.

Explore how to expand the polynomial g(x) = 3(x+1)(x+3)(x-4) into standard form, determine its degree as 3, and identify the constant term -36. This example demonstrates polynomial expansion techniques suitable for high school students learning algebra.

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