Perform the indicated operations. (10m⁴-4m²)/2m

Verified step by step guidance

1. Start by writing the expression clearly: \(\frac{10m^4 - 4m^2}{2m}\).
2. Recognize that the numerator is a difference of two terms, so you can split the fraction into two separate fractions: \(\frac{10m^4}{2m} - \frac{4m^2}{2m}\).
3. Simplify each fraction separately by dividing the coefficients and subtracting the exponents of like bases: For \(\frac{10m^4}{2m}\), divide 10 by 2 and subtract the exponents of \(m\) (4 - 1). For \(\frac{4m^2}{2m}\), divide 4 by 2 and subtract the exponents of \(m\) (2 - 1).
4. Write the simplified terms after performing the division and exponent subtraction: \(5m^{(4-1)} - 2m^{(2-1)}\).
5. Simplify the exponents to get the final expression in terms of powers of \(m\): \(5m^3 - 2m\).

Key Concepts

Polynomial Expressions

Polynomial expressions are algebraic expressions consisting of variables raised to whole-number exponents and coefficients. Understanding how to identify terms and their degrees is essential for simplifying or performing operations on polynomials.

Division of Polynomials

Dividing polynomials involves dividing each term of the numerator by the denominator separately when the denominator is a monomial. This process simplifies the expression by reducing powers and coefficients accordingly.

Exponent Rules

Exponent rules govern how to handle powers during multiplication and division. Specifically, when dividing like bases, subtract the exponents (e.g., a^m / a^n = a^(m-n)), which is crucial for simplifying terms in polynomial division.