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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2b66b4e-bafc-41a8-9620-24f5d41483ef%2F159d4cfb-93a3-484a-af08-789833a6c860%2Fgdkh5ml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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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