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 nonnegative 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

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

Apply the rule of exponents: When dividing powers with the same base, subtract the exponents. = (1/2)x^(63)  2x^(53)  (7/2)x^(33)

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).