Math Problem Statement

Determine the coefficient of each​ term, the degree of each​ term, the degree of the​ polynomial, the leading​ term, and the leading coefficient of the following polynomial.

x cubed plus x squaredx3+x2

Question content area bottom

Part 1

The coefficient of the term

x cubedx3

is

enter your response here.

Part 2

The degree of the term

x cubedx3

is

enter your response here.

Part 3

The coefficient of the term

x squaredx2

is

enter your response here.

Part 4

The degree of the term

x squaredx2

is

enter your response here.

Part 5

The degree of the polynomial is

enter your response here.

Part 6

The leading term of the polynomial is

enter your response here.

Part 7

The leading coefficient of the polynomial is

enter your response here.

Solution

Let's break down the polynomial x3+x2x^3 + x^2 and determine the required information.

Part 1: Coefficient of x3x^3

The coefficient of the term x3x^3 is 11, since x3x^3 is equivalent to 1x31 \cdot x^3.

Part 2: Degree of x3x^3

The degree of the term x3x^3 is 33, which is the exponent of xx.

Part 3: Coefficient of x2x^2

The coefficient of the term x2x^2 is 11, since x2x^2 is equivalent to 1x21 \cdot x^2.

Part 4: Degree of x2x^2

The degree of the term x2x^2 is 22, which is the exponent of xx.

Part 5: Degree of the Polynomial

The degree of the polynomial x3+x2x^3 + x^2 is the highest degree of its terms, which is 33.

Part 6: Leading Term of the Polynomial

The leading term of the polynomial x3+x2x^3 + x^2 is the term with the highest degree, which is x3x^3.

Part 7: Leading Coefficient of the Polynomial

The leading coefficient of the polynomial x3+x2x^3 + x^2 is the coefficient of the leading term, which is 11.

Here is a summary of all parts:

  1. Coefficient of x3x^3: 11
  2. Degree of x3x^3: 33
  3. Coefficient of x2x^2: 11
  4. Degree of x2x^2: 22
  5. Degree of the Polynomial: 33
  6. Leading Term of the Polynomial: x3x^3
  7. Leading Coefficient of the Polynomial: 11

Would you like more details on any part, or do you have any further questions?

Questions for further exploration:

  1. What is the coefficient of xx in the polynomial 2x3+4x2+3x+52x^3 + 4x^2 + 3x + 5?
  2. How do you determine the degree of a polynomial with multiple terms?
  3. What is the leading term of the polynomial 7x5+3x3x+9-7x^5 + 3x^3 - x + 9?
  4. What is the degree of the polynomial x4+2x3+x2+x+1x^4 + 2x^3 + x^2 + x + 1?
  5. How do you find the coefficient of a specific term in a polynomial?
  6. What is the leading coefficient of the polynomial 5x32x2+x85x^3 - 2x^2 + x - 8?
  7. How does the degree of a polynomial affect its graph?
  8. What is the general form of a polynomial of degree nn?

Tip:

When determining the degree of a polynomial, always look for the term with the highest exponent. This highest exponent indicates the degree of the polynomial.

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Math Problem Analysis

Mathematical Concepts

Polynomials
Degrees of Terms
Leading Coefficient
Leading Term

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9