Perform the indicated operations. (10m^4-4m^2)/2m

Verified step by step guidance

1. First, observe the expression \( \frac{10m^4 - 4m^2}{2m} \). We need to simplify this by performing the division.
2. Factor out the greatest common factor from the numerator, which is \( 2m^2 \). This gives us \( 2m^2(5m^2 - 2) \).
3. Rewrite the expression as \( \frac{2m^2(5m^2 - 2)}{2m} \).
4. Cancel the common factor \( 2m \) from the numerator and the denominator. This simplifies to \( m(5m^2 - 2) \).
5. Distribute \( m \) across the terms inside the parentheses to get the final simplified expression.

Key Concepts

Polynomial Operations

Polynomial operations involve performing arithmetic operations such as addition, subtraction, multiplication, and division on polynomial expressions. In this case, the expression (10m^4 - 4m^2) is a polynomial, and understanding how to manipulate polynomials is essential for simplifying or factoring them correctly.

Factoring

Factoring is the process of breaking down a polynomial into simpler components, or factors, that can be multiplied together to yield the original polynomial. In the given expression, recognizing common factors can simplify the operation before division, making it easier to work with the polynomial.

Rational Expressions

Rational expressions are fractions where the numerator and/or denominator are polynomials. Understanding how to simplify rational expressions, such as dividing a polynomial by another polynomial, is crucial for solving the problem. This involves canceling common factors and ensuring the expression is in its simplest form.