Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Multiplying Polynomials

College Algebra

0. Review of Algebra

Multiplying Polynomials

1:16 minutes

Problem 23b

Textbook Question

Add or subtract, as indicated. See Example 2. (5x^2-4x+7) + (-4x^2+3x-5)

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Key Concepts

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

Polynomial Addition

Polynomial addition involves combining like terms from two or more polynomials. Like terms are those that have the same variable raised to the same power. For example, in the expression (5x^2 - 4x + 7) + (-4x^2 + 3x - 5), you would add the coefficients of x^2, x, and the constant terms separately to simplify the expression.

Like Terms

Like terms are terms in a polynomial that share the same variable and exponent. For instance, in the expression 5x^2 and -4x^2 are like terms because they both contain x raised to the power of 2. Identifying and combining like terms is essential for simplifying polynomial expressions accurately.

Combining Polynomials

Combining polynomials requires careful attention to the signs and coefficients of each term. When adding or subtracting polynomials, it is crucial to distribute any negative signs correctly and ensure that all like terms are accounted for. This process leads to a simplified polynomial that represents the sum or difference of the original expressions.