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

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1:53 minutes

Problem 25

Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor.−8x − 48

Verified step by step guidance

Identify the greatest common factor (GCF) of the terms in the expression \(-8x - 48\).

The GCF of \(-8x\) and \(-48\) is \(8\).

Factor out the negative of the GCF, which is \(-8\), from each term in the expression.

Rewrite the expression as \(-8(x + 6)\).

Verify the factorization by distributing \(-8\) back into the expression to ensure it equals 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 that divides two or more numbers without leaving a remainder. To find the GCF, one can list the factors of each number and identify the highest one. In the expression −8x − 48, the GCF is 8, as both terms can be divided by 8.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In this case, factoring out the GCF involves rewriting the expression in a way that highlights the common factor, making it easier to simplify or solve.

Negative Factor

Factoring out a negative involves taking the negative of the GCF and using it to rewrite the expression. This is important for maintaining the sign of the original expression. In the given problem, factoring out -8 from −8x − 48 results in -8(x + 6), which simplifies the expression while keeping its value intact.