**4. For the following polynomial, write the polynomial in standard form and specify:** a) its degree b) constant term c) Explain whether the function is even or odd and describe the end behavior. \[ p(x) = (x + 1)(x - 2)(x - 4) \]**Detailed Explanation:**1. **Standard Form:** To express \( p(x) \) in standard form, we need to expand the given polynomial: \[ p(x) = (x + 1)(x - 2)(x - 4) \] - First, expand \((x + 1)(x - 2)\): \[ (x + 1)(x - 2) = x^2 - 2x + x - 2 = x^2 - x - 2 \] - Now, expand \( (x^2 - x - 2)(x - 4) \): \[ (x^2 - x - 2)(x - 4) = x^3 - 4x^2 - x^2 + 4x - 2x + 8 = x^3 - 5x^2 + 6x + 8 \] Hence, the standard form of the polynomial is: \[ p(x) = x^3 - 7x^2 + 6x + 8 \]2. **Degree:** The degree of a polynomial is the highest power of the variable \( x \) in the polynomial. For \( p(x) = x^3 - 7x^2 + 6x + 8 \), the highest power of \( x \) is 3. Therefore, the degree of the polynomial is: \[ \text{Degree} = 3 \]3. **Constant Term:** The constant term in a polynomial is the term without any variable \( x \). In the polynomial \( p(x) = x^3 - 7x^2 + 6x + 8 \), the constant term is: \[ \text{Constant Term} = 8 \]4. **Even or Odd Function:** To determine if the function is even, odd, or neither, we analyze the

Expand the polynomial then answer the questions.

4. For the following polynomial write the polynomial in standard form and specify: a) its degree b) constant term c) Explain whether function is even or odd and describe end behavior. p(x) = (x + 1)(x - 2)(x-4)

4. For the following polynomial write the polynomial in standard form and specify: a) its degree b) constant term c) Explain whether function is even or odd and describe end behavior. p(x) = (x + 1)(x - 2)(x-4)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**4. For the following polynomial, write the polynomial in standard form and specify:**
a) its degree
b) constant term
c) Explain whether the function is even or odd and describe the end behavior.

\[ p(x) = (x + 1)(x - 2)(x - 4) \]

**Detailed Explanation:**

1. **Standard Form:**
To express \( p(x) \) in standard form, we need to expand the given polynomial:

\[ p(x) = (x + 1)(x - 2)(x - 4) \]

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

- Now, expand \( (x^2 - x - 2)(x - 4) \):
\[
(x^2 - x - 2)(x - 4) = x^3 - 4x^2 - x^2 + 4x - 2x + 8 = x^3 - 5x^2 + 6x + 8
\]

Hence, the standard form of the polynomial is:
\[
p(x) = x^3 - 7x^2 + 6x + 8
\]

2. **Degree:**
The degree of a polynomial is the highest power of the variable \( x \) in the polynomial. For \( p(x) = x^3 - 7x^2 + 6x + 8 \), the highest power of \( x \) is 3. Therefore, the degree of the polynomial is:
\[
\text{Degree} = 3
\]

3. **Constant Term:**
The constant term in a polynomial is the term without any variable \( x \). In the polynomial \( p(x) = x^3 - 7x^2 + 6x + 8 \), the constant term is:
\[
\text{Constant Term} = 8
\]

4. **Even or Odd Function:**
To determine if the function is even, odd, or neither, we analyze the

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