https://file.aiquickdraw.com/mathbot/file/17266184770497b9hu8bi.jpg

Let's work through the problem in the image step by step.

### Question 2a
We are given the polynomial function:

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

### To rewrite this polynomial in standard form:
We'll expand the factored form to get a polynomial of the form \( ax^n + bx^{n-1} + \dots \).

#### Step 1: Multiply the first two factors:
\[
(x + 1)(x + 3) = x^2 + 3x + x + 3 = x^2 + 4x + 3
\]

#### Step 2: Now, multiply the result by the third factor \((x - 4)\):
\[
(x^2 + 4x + 3)(x - 4)
\]

Distribute each term of \(x^2 + 4x + 3\) to \(x - 4\):

\[
x^2(x - 4) = x^3 - 4x^2
\]
\[
4x(x - 4) = 4x^2 - 16x
\]
\[
3(x - 4) = 3x - 12
\]

#### Step 3: Combine all the terms:
\[
x^3 - 4x^2 + 4x^2 - 16x + 3x - 12
\]

Simplify:
\[
f(x) = x^3 - 13x - 12
\]

### Degree and constant term:
- **Degree**: The highest power of \(x\) is 3, so the degree is 3.
- **Constant term**: The constant term is the term without \(x\), which is \(-12\).

### Final Answer:
\[
f(x) = x^3 - 13x - 12
\]
- Degree: 3
- Constant term: \(-12\)

---

Do you have any questions or would you like further clarification on this solution?

Here are 5 related questions for further practice:
1. Expand and simplify \( f(x) = (x - 2)(x + 5)(x - 1) \).
2. What is the degree and constant term of the polynomial \( f(x) = (x - 3)(x + 2)(x + 4) \)?
3. How would the graph of \( f(x) = (x + 1)(x + 3)(x - 4) \) look based on its roots and degree?
4. Rewrite \( f(x) = (x + 1)(x + 2)(x + 3)(x - 4) \) in standard form.
5. What is the behavior of the polynomial \( f(x) = x^3 - 13x - 12 \) as \(x\) approaches positive and negative infinity?

### Tip:
When expanding polynomials, distribute carefully and keep track of all terms to avoid mistakes in combining like terms!

For each polynomial function, rewrite the polynomial in standard form and identify the degree and constant term.

f(x) = (x + 1)(x + 3)(x - 4)

Learn how to rewrite the polynomial function f(x) = (x + 1)(x + 3)(x - 4) in standard form by expanding it step by step. Identify the degree and constant term for this cubic polynomial, and understand key concepts such as the distributive property and polynomial degree.

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