Question

consider the following polynomial:

\\x^4 - 5x + 2x^3 + x^2 - 9\\

the coefficient of the linear term is

the coefficient of the quadratic term is

the coefficient of the cubic term is

Explanation:

🆕 New Concept Discovered: Polynomial Terms and Coefficients
Identifying parts of a polynomial by their degree.

Step 1: Identify the linear term

The linear term is the term where the variable \(x\) has an exponent of 1 (written simply as \(x\)).

In the polynomial \(x^4 - 5x + 2x^3 + x^2 - 9\), the linear term is:
\[-5x\]

The coefficient is the number multiplying the variable, including its sign:
\[-5\]

Step 2: Identify the quadratic term

The quadratic term is the term where the variable \(x\) is raised to the power of 2 (\(x^2\)).

In the polynomial, the quadratic term is:
\[x^2\]

Since there is no visible number in front of \(x^2\), its coefficient is understood to be:
\[1\]

Step 3: Identify the cubic term

The cubic term is the term where the variable \(x\) is raised to the power of 3 (\(x^3\)).

In the polynomial, the cubic term is:
\[2x^3\]

The coefficient of this term is:
\[2\]

Answer:

• The coefficient of the linear term is -5
• The coefficient of the quadratic term is 1
• The coefficient of the cubic term is 2