Math Problem Statement

Answer the questions about the following polynomial: 8x^3 + 6x -1 What expression polynomial is it? How many terms are there and what are the terms? What is the constant term? What are the leading term, the coefficient?

Solution

Let's break down the polynomial 8x3+6x18x^3 + 6x - 1 and answer the questions one by one.

1. What expression polynomial is it?

This is a cubic polynomial. It has a degree of 3 (the highest power of xx).

2. How many terms are there and what are the terms?

The polynomial has 3 terms:

  • 8x38x^3 (cubic term)
  • 6x6x (linear term)
  • 1-1 (constant term)

3. What is the constant term?

The constant term is 1-1. This term has no variable (xx).

4. What are the leading term and the coefficient?

The leading term is the term with the highest degree of xx, which is 8x38x^3.

The coefficient of the leading term is 8, which is the numerical factor in front of x3x^3.


Would you like more details on any of these points? Or would you like to explore related concepts further?

Here are some follow-up questions:

  1. What does the degree of a polynomial tell you?
  2. How do you find the degree of a polynomial?
  3. What is the difference between the leading term and the constant term?
  4. How can you factor a cubic polynomial like 8x3+6x18x^3 + 6x - 1?
  5. How do you determine the degree of the polynomial when terms have different powers of xx?

Tip: When identifying the degree of a polynomial, always look for the term with the highest power of the variable.