Math Problem Statement

Rewrite the following polynomial in standard form. x, minus, 3, plus, 10, x, cubed, minus, start fraction, x, to the power 5 , divided by, 9, end fraction x−3+10x 3 − 9 x 5

Solution

Let's rewrite the given polynomial in standard form. The standard form of a polynomial lists terms in descending powers of xx.

Given polynomial:

x3+10x3x59x - 3 + 10x^3 - \frac{x^5}{9}

To express it in standard form, arrange the terms by powers of xx, from the highest power to the lowest:

x59+10x3+x3-\frac{x^5}{9} + 10x^3 + x - 3

The standard form of the polynomial is:

19x5+10x3+x3-\frac{1}{9}x^5 + 10x^3 + x - 3

Would you like more details on how to interpret or manipulate polynomials? Here are some related questions you might find interesting:

  1. How do you identify the degree of a polynomial?
  2. What are the different types of polynomials based on their degrees?
  3. How do you add or subtract polynomials in standard form?
  4. What is the concept of a leading term in a polynomial?
  5. How do you perform synthetic division on polynomials?

Tip: To easily combine polynomials, always ensure like terms (same powers of xx) are grouped together.

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Math Problem Analysis

Mathematical Concepts

Polynomials
Standard Form of Polynomials
Algebra

Formulas

Standard form of a polynomial: Terms arranged by descending powers of x

Theorems

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Suitable Grade Level

Grades 8-10