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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 10
Chapter 1, Problem 10

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

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

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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