Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. 9
Table of contents
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Multiplying Polynomials
Problem 10
Textbook Question
Perform the indicated operations. (10m4-4m2)/2m
Verified step by step guidance1
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$.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
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.
Recommended video:
Guided course
Introduction to Algebraic Expressions
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.
Recommended video:
Guided course
Introduction to Polynomials
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.
Recommended video:
Guided course
Introduction to Exponent Rules
Related Videos
Related Practice
Textbook Question
33
views
