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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1:17 minutes

Problem 99

Textbook Question

Factor by any method. See Examples 1–7. p^4(m-2n)+q(m-2n)

Verified step by step guidance

Identify the common factor in the expression: \((m - 2n)\).

Factor out the common factor \((m - 2n)\) from each term in the expression.

Rewrite the expression as \((m - 2n)(p^4 + q)\).

Verify the factorization by distributing \((m - 2n)\) back into \((p^4 + q)\) to ensure it matches the original expression.

Conclude that the expression is factored as \((m - 2n)(p^4 + q)\).

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Key Concepts

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

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. This is a fundamental skill in algebra, allowing for simplification and solving of equations. Common methods include factoring out the greatest common factor (GCF), using the difference of squares, and applying the quadratic formula.

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest factor that two or more terms share. Identifying the GCF is crucial in factoring expressions, as it allows for the simplification of the expression by pulling out the common factor. For example, in the expression p^4(m-2n) + q(m-2n), the GCF is (m-2n), which can be factored out to simplify the expression.

Polynomial Expressions

Polynomial expressions are algebraic expressions that consist of variables raised to non-negative integer powers and their coefficients. They can have one or more terms, and factoring polynomials is essential for solving equations and simplifying expressions. Understanding the structure of polynomials helps in recognizing patterns and applying appropriate factoring techniques.