Math Problem Statement

Consider the polynomial 2x^5 + 4x^3 - 3x^8. Select the polynomial in standard form.

Solution

The given polynomial is:

2x5+4x33x82x^5 + 4x^3 - 3x^8

To write the polynomial in standard form, the terms should be arranged in descending order of their exponents.

So, in this case, the term with the highest power of xx is 3x8-3x^8, followed by 2x52x^5, and finally 4x34x^3.

The polynomial in standard form is:

3x8+2x5+4x3-3x^8 + 2x^5 + 4x^3

Would you like further details or any additional clarifications?

Here are some related questions to expand your understanding:

  1. What is the degree of the polynomial 3x8+2x5+4x3-3x^8 + 2x^5 + 4x^3?
  2. How do you determine the leading coefficient of a polynomial?
  3. Can you explain the difference between a monomial, binomial, and polynomial?
  4. What are the steps to factor a polynomial?
  5. How can you apply the polynomial in standard form to solve a real-world problem?

Tip: Always check the exponents and arrange terms from the highest to lowest power when converting a polynomial to standard form.

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Math Problem Analysis

Mathematical Concepts

Polynomial
Standard Form
Algebra

Formulas

Standard form of a polynomial involves arranging terms in descending order of their exponents.

Theorems

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Suitable Grade Level

Grades 8-10