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

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

1:46 minutes

Problem 43a

Textbook Question

In Exercises 35–44, factor the greatest common binomial factor from each polynomial. (x + 2)(x + 3) + (x − 1)(x + 3)

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Key Concepts

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

Factoring Polynomials

Factoring polynomials involves breaking down a polynomial into simpler components, or factors, that when multiplied together yield the original polynomial. This process is essential for simplifying expressions and solving equations. In this case, recognizing common factors in the given polynomial expression is crucial for effective factoring.

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or expressions without leaving a remainder. In polynomial expressions, identifying the GCF allows for the simplification of the expression by factoring it out, making it easier to work with. This concept is key to solving the problem presented.

Binomial Expressions

A binomial expression is a polynomial that consists of two terms, typically connected by a plus or minus sign. In the context of the given problem, recognizing the binomial factors within the polynomial is essential for factoring out the GCF. Understanding how to manipulate and factor binomials is a fundamental skill in algebra.