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(x^6-4x^5-7x^3)/(2x^3)

2 min read Jun 17, 2024
(x^6-4x^5-7x^3)/(2x^3)

Simplifying the Expression (x^6 - 4x^5 - 7x^3) / (2x^3)

This expression involves dividing a polynomial by a monomial. Here's how to simplify it:

Understanding the Concept

  • Polynomial: An expression with multiple terms, each consisting of a coefficient and a variable raised to a non-negative integer power.
  • Monomial: A polynomial with only one term.
  • Division of Polynomials: When dividing a polynomial by a monomial, we divide each term of the polynomial individually by the monomial.

Steps to Simplify

  1. Separate the terms: (x^6 - 4x^5 - 7x^3) / (2x^3) = (x^6 / 2x^3) - (4x^5 / 2x^3) - (7x^3 / 2x^3)

  2. Apply the rule of exponents: When dividing powers with the same base, subtract the exponents. = (1/2)x^(6-3) - 2x^(5-3) - (7/2)x^(3-3)

  3. Simplify: = (1/2)x^3 - 2x^2 - (7/2)

Final Result

Therefore, the simplified form of the expression (x^6 - 4x^5 - 7x^3) / (2x^3) is (1/2)x^3 - 2x^2 - (7/2).

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