Table of contents

0. Review of Algebra4h 18m

Algebraic Expressions
36m

Exponents
32m

Polynomials Intro
19m

Multiplying Polynomials
36m

Factoring Polynomials
1h 2m

Radical Expressions
15m

Simplifying Radical Expressions
35m

Rationalize Denominator
15m

Rational Exponents
4m

1. Equations & Inequalities3h 18m

Linear Equations
31m

Rational Equations
21m

The Imaginary Unit
6m

Powers of i
11m

Complex Numbers
36m

Intro to Quadratic Equations
18m

The Square Root Property
11m

Completing the Square
12m

The Quadratic Formula
18m

Choosing a Method to Solve Quadratics
9m

Linear Inequalities
20m

2. Graphs of Equations1h 43m

Graphs and Coordinates
7m

Two-Variable Equations
23m

Lines
1h 12m

3. Functions2h 17m

Intro to Functions & Their Graphs
35m

Common Functions
5m

Transformations
45m

Function Operations
21m

Function Composition
29m

4. Polynomial Functions1h 44m

Quadratic Functions
39m

Understanding Polynomial Functions
34m

Graphing Polynomial Functions
30m

Dividing Polynomials

Zeros of Polynomial Functions

5. Rational Functions1h 23m

Introduction to Rational Functions
9m

Asymptotes
35m

Graphing Rational Functions
38m

6. Exponential & Logarithmic Functions2h 28m

Introduction to Exponential Functions
9m

Graphing Exponential Functions
25m

The Number e
8m

Introduction to Logarithms
22m

Graphing Logarithmic Functions
18m

Properties of Logarithms
27m

Solving Exponential and Logarithmic Equations
35m

7. Systems of Equations & Matrices4h 5m

Two Variable Systems of Linear Equations
1h 7m

Introduction to Matrices
1h 11m

Determinants and Cramer's Rule
1h 3m

Graphing Systems of Inequalities
42m

8. Conic Sections2h 23m

Introduction to Conic Sections
5m

Circles
15m

Ellipses: Standard Form
33m

Parabolas
36m

Hyperbolas at the Origin
40m

Hyperbolas NOT at the Origin
12m

9. Sequences, Series, & Induction1h 22m

Sequences
40m

Arithmetic Sequences
25m

Geometric Sequences
15m

10. Combinatorics & Probability1h 45m

Factorials
11m

Combinatorics
46m

Probability
47m

0. Review of Algebra

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

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2:02 minutes

Problem 27

Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor.−2x² + 6x − 14

Verified step by step guidance

Identify the greatest common factor (GCF) of the terms in the expression $-2x^2 + 6x - 14$.

The GCF of the coefficients $-2$, $6$, and $-14$ is $2$.

Factor out $-2$ from each term in the expression.

Rewrite the expression as $-2(x^2 - 3x + 7)$.

Verify by distributing $-2$ back through the expression to ensure it matches the original expression.

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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 each term of a polynomial without leaving a remainder. To find the GCF, identify the common factors of the coefficients and the variables in each term. In the expression −2x² + 6x − 14, the GCF is -2, as it is the highest factor that can be factored out from all terms.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and can help solve equations. In this case, factoring out the GCF allows us to express the polynomial in a simpler form, making it easier to analyze or solve. The goal is to express the polynomial in a way that highlights its structure.

Negative Sign in Factoring

Factoring out a negative sign means that we are extracting a negative value from the polynomial, which can change the signs of the terms. This is particularly useful when the leading coefficient is negative, as it can simplify the expression and make it easier to work with. In the given polynomial, factoring out -2 not only simplifies the expression but also ensures that the leading coefficient of the resulting polynomial is positive.

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