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