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

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

Previous problemNext problem

2:24 minutes

Problem 23

Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. (5r-6)(r+3)-(2r-1)(r+3)

Verified step by step guidance

Identify the common factor in the expression: Notice that both terms, \((5r-6)(r+3)\) and \((2r-1)(r+3)\), have a common binomial factor \((r+3)\).

Factor out the common binomial \((r+3)\) from the entire expression: This means you will write the expression as \((r+3)\) multiplied by another expression.

Write the remaining expression after factoring out \((r+3)\): After factoring out \((r+3)\), you are left with \((5r-6) - (2r-1)\).

Simplify the expression inside the parentheses: Distribute the negative sign in \((2r-1)\) to get \(5r - 6 - 2r + 1\).

Combine like terms: Combine \(5r\) and \(-2r\), and \(-6\) and \(+1\) to simplify the expression further.

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.

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest integer or algebraic expression that divides two or more terms without leaving a remainder. To find the GCF, one must identify the common factors of the coefficients and the variables in the terms. This concept is essential for simplifying expressions and factoring polynomials effectively.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors, which can include numbers, variables, or other polynomials. This process often simplifies expressions and makes it easier to solve equations. Recognizing patterns, such as the difference of squares or common binomials, is crucial in this step.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac, allowing one to multiply a single term by each term within a parenthesis. This property is fundamental in expanding expressions and is often used in the process of factoring, as it helps to identify common factors across terms in a polynomial.