Questions: Week 2 Quiz (Retake) Score: 2/5 2/5 answered Question 3 Characteristics of Polynomials For each Polynomial, identify its key characteristics. Polynomial Name Leading Coefficient Constant Term Degree 8x^7+x^6+3 Select an answer v -x+4 Select an answer v 7x^4 Select an answer v

Week 2 Quiz (Retake)
Score: 2/5 2/5 answered

Question 3
Characteristics of Polynomials
For each Polynomial, identify its key characteristics.
Polynomial Name Leading Coefficient Constant Term Degree
8x^7+x^6+3 Select an answer v
-x+4 Select an answer v
7x^4 Select an answer v

Transcript text: Week 2 Quiz (Retake) Score: 2/5 2/5 answered Question 3 \begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{5}{|c|}{Characteristics of Polynomials} \\ \hline \multicolumn{5}{|l|}{For each Polynomial, identify its key characteristics.} \\ \hline Polynomial & Name & Leading Coefficient & \begin{tabular}{l} Constant \\ Term \end{tabular} & Degree \\ \hline $8 x^{7}+x^{6}+3$ & Select an answer $v$ & & & \\ \hline $-x+4$ & Select an answerv & & & \\ \hline $7 x^{4}$ & Select an answer $\vee$ & & & \\ \hline \end{tabular}

Solution

Solution Steps

To identify the key characteristics of each polynomial, we need to determine the following for each polynomial: the name (based on its degree), the leading coefficient (the coefficient of the term with the highest degree), the constant term (the term without a variable), and the degree (the highest power of the variable).

To solve the given problem, we need to identify the key characteristics of each polynomial listed in the table. These characteristics include the name of the polynomial, the leading coefficient, the constant term, and the degree of the polynomial.

Step 1: Analyze the Polynomial $8x^7 + x^6 + 3$

Name: This is a polynomial of degree 7, so it is called a "septic" or "7th degree" polynomial.
Leading Coefficient: The leading term is $8x^7$, so the leading coefficient is 8.
Constant Term: The constant term is the term without a variable, which is 3.
Degree: The highest power of $x$ is 7, so the degree is 7.

Step 2: Analyze the Polynomial $-x + 4$

Name: This is a polynomial of degree 1, so it is called a "linear" polynomial.
Leading Coefficient: The leading term is $-x$, so the leading coefficient is -1.
Constant Term: The constant term is 4.
Degree: The highest power of $x$ is 1, so the degree is 1.

Step 3: Analyze the Polynomial $7x^4$

Name: This is a polynomial of degree 4, so it is called a "quartic" or "4th degree" polynomial.
Leading Coefficient: The leading term is $7x^4$, so the leading coefficient is 7.
Constant Term: There is no constant term, so it is 0.
Degree: The highest power of $x$ is 4, so the degree is 4.

Final Answer

For each polynomial, the key characteristics are:

Polynomial: $8x^7 + x^6 + 3$
- Name: Septic
- Leading Coefficient: 8
- Constant Term: 3
- Degree: 7
- $\boxed{\text{Name: Septic, Leading Coefficient: 8, Constant Term: 3, Degree: 7}}$
Polynomial: $-x + 4$
- Name: Linear
- Leading Coefficient: -1
- Constant Term: 4
- Degree: 1
- $\boxed{\text{Name: Linear, Leading Coefficient: -1, Constant Term: 4, Degree: 1}}$
Polynomial: $7x^4$
- Name: Quartic
- Leading Coefficient: 7
- Constant Term: 0
- Degree: 4
- $\boxed{\text{Name: Quartic, Leading Coefficient: 7, Constant Term: 0, Degree: 4}}$

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