Textbook Question
Use set notation, and list all the elements of each set. {74, 68, 62, ..., 38}
3
views
Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
Not the one you use?Change textbookSelect a different textbook
Table of contents
Chapter 1, Problem 24
Add or subtract, as indicated.
Verified step by step guidance1
Identify the polynomials to be added: \( (3m^5 - 3m^2 + 4) \) and \( (-2m^3 - m^2 + 6) \).
Remove the parentheses and write the expression as a single sum: \( 3m^5 - 3m^2 + 4 - 2m^3 - m^2 + 6 \).
Group like terms together. Like terms have the same variable raised to the same power: \( 3m^5 + (-2m^3) + (-3m^2 - m^2) + (4 + 6) \).
Combine the coefficients of the like terms by performing the indicated addition or subtraction: \( 3m^5 - 2m^3 - 4m^2 + 10 \).
Write the simplified polynomial as the final answer, ensuring terms are in descending order of exponents.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Addition and Subtraction
Adding or subtracting polynomials involves combining like terms, which are terms with the same variable raised to the same power. You add or subtract their coefficients while keeping the variable part unchanged. This process simplifies the expression into a single polynomial.
Recommended video:
Guided course
03:34
Adding and Subtracting Polynomials
Like Terms
Like terms are terms in a polynomial that have identical variable parts, including the same exponents. For example, 3m^5 and 5m^5 are like terms, but 3m^5 and 2m^3 are not. Recognizing like terms is essential for correctly combining terms during addition or subtraction.
Recommended video:
Guided course
03:50Adding & Subtracting Like Radicals
Polynomial Notation and Exponents
Polynomials are expressions consisting of variables raised to whole-number exponents and coefficients. Understanding the notation, such as m^5 meaning m raised to the fifth power, helps in identifying like terms and performing operations correctly.
Recommended video:
Guided course
04:06Rational Exponents
Related Practice
Textbook Question
Write each rational expression in lowest terms. 3(3 - t) / (t + 5)(t - 3)
1
views
Textbook Question
Add or subtract, as indicated.
Textbook Question
Factor out the greatest common factor from each polynomial. See Example 1. 2(m-1)-3(m-1)2+2(m-1)3
Textbook Question
Simplify each expression. Assume all variables represent nonzero real numbers. (64)3
4
views
Textbook Question
Factor out the greatest common factor from each polynomial. See Example 1. (4z-5)(3z-2)-(3z-9)(3z-2)