Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Multiplying Polynomials

College Algebra

0. Review of Algebra

Multiplying Polynomials

Previous problemNext problem

1:26 minutes

Problem 24

Textbook Question

Add or subtract, as indicated. See Example 2. (3m^5-3m^2+4) + (-2m^3-m^2+6)

Verified step by step guidance

Identify the like terms in the expression. Like terms are terms that have the same variable raised to the same power.

Group the like terms together. In this case, group the terms with the same powers of m.

Combine the coefficients of the like terms. For example, add or subtract the coefficients of the m^2 terms.

Write the simplified expression by combining the results from the previous step.

Ensure that the expression is in standard form, which means writing the terms in descending order of their exponents.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Polynomial Addition and Subtraction

Polynomial addition and subtraction involve combining like terms from two or more polynomials. Like terms are those that have the same variable raised to the same power. When adding or subtracting, you simply add or subtract the coefficients of these like terms while keeping the variable part unchanged.

Like Terms

Like terms are terms in a polynomial that share the same variable and exponent. For example, in the expression 3m^5 and -2m^5, both terms are like terms because they both contain the variable m raised to the fifth power. Identifying like terms is crucial for simplifying polynomials correctly during addition or subtraction.

Combining Polynomials

Combining polynomials requires careful organization of terms to ensure accurate calculations. When combining, it is helpful to group like terms together before performing the addition or subtraction. This method not only simplifies the process but also helps in avoiding errors, ensuring that the final polynomial is expressed in standard form.