Question

type your response in the box.

describe each polynomial expression by type and components based on the example shown.

• (3x^2 + 2x)
• (2x^2 - 5x + 3)
• (6x)

example: (-4x^2 + 9)

this polynomial expression is a quadratic binomial, with a coefficient of -4 on the quadratic term, a constant of 9, and no linear terms.

Explanation:

🆕 New Concept Discovered: Classifying Polynomials
Naming polynomials by degree and number of terms.

Step 1: Analyze the Example Structure

The example provided is:

• Expression: \( -4x^2 + 9 \)
• Description: "This polynomial expression is a quadratic binomial, with a coefficient of -4 on the quadratic term, a constant of 9, and no linear terms."

To describe each expression, we need to identify:

1. Degree (e.g., quadratic for degree 2, linear for degree 1).
2. Number of terms (e.g., monomial for 1 term, binomial for 2 terms, trinomial for 3 terms).
3. Components: The coefficients of the quadratic term (\( x^2 \)), the linear term (\( x \)), and the constant term.

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Step 2: Describe \( 3x^2 + 2x \)

• Type: It has a degree of 2 (quadratic) and 2 terms (binomial). So, it is a quadratic binomial.
• Components:
• Coefficient of \( 3 \) on the quadratic term.
• Coefficient of \( 2 \) on the linear term.
• No constant term.

Description:
This polynomial expression is a quadratic binomial, with a coefficient of 3 on the quadratic term, a coefficient of 2 on the linear term, and no constant term.

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Step 3: Describe \( 2x^2 - 5x + 3 \)

• Type: It has a degree of 2 (quadratic) and 3 terms (trinomial). So, it is a quadratic trinomial.
• Components:
• Coefficient of \( 2 \) on the quadratic term.
• Coefficient of \( -5 \) on the linear term.
• A constant of \( 3 \).

Description:
This polynomial expression is a quadratic trinomial, with a coefficient of 2 on the quadratic term, a coefficient of -5 on the linear term, and a constant of 3.

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Step 4: Describe \( 6x \)

• Type: It has a degree of 1 (linear) and 1 term (monomial). So, it is a linear monomial.
• Components:
• Coefficient of \( 6 \) on the linear term.
• No quadratic term.
• No constant term.

Description:
This polynomial expression is a linear monomial, with a coefficient of 6 on the linear term, no quadratic term, and no constant term.

Answer:

• \( 3x^2 + 2x \): This polynomial expression is a quadratic binomial, with a coefficient of 3 on the quadratic term, a coefficient of 2 on the linear term, and no constant term.
• \( 2x^2 - 5x + 3 \): This polynomial expression is a quadratic trinomial, with a coefficient of 2 on the quadratic term, a coefficient of -5 on the linear term, and a constant of 3.
• \( 6x \): This polynomial expression is a linear monomial, with a coefficient of 6 on the linear term, no quadratic term, and no constant term.