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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 97
Chapter 1, Problem 97

Factor by any method. See Examples 1–7. x2+xy-5x-5y

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1
Group the terms in pairs to make factoring easier: \((x^2 + xy) - (5x + 5y)\).
Factor out the greatest common factor (GCF) from each group: \(x(x + y) - 5(x + y)\).
Notice that both terms contain the common binomial factor \((x + y)\).
Factor out the common binomial \((x + y)\): \((x + y)(x - 5)\).
The expression is now factored completely as \((x + y)(x - 5)\).

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Key Concepts

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

Factoring by Grouping

Factoring by grouping involves rearranging and grouping terms in a polynomial to find common factors within each group. This method is useful when a polynomial has four terms, allowing you to factor out common binomials and simplify the expression.
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Common Factors

Identifying common factors means finding terms or expressions that appear in multiple parts of a polynomial. Extracting these common factors simplifies the polynomial and is a crucial step in factoring complex expressions.
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Polynomial Terms and Variables

Understanding polynomial terms and variables is essential for factoring. Each term consists of coefficients and variables raised to powers, and recognizing how these combine helps in grouping and factoring the expression correctly.
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Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. (M ∩ N) ∪ R

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Textbook Question

Evaluate each expression. −8+(−4)(−6)÷124−(−3)\(\frac{-8 + (-4)(-6) \div 12}{4 - (-3)}\)

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Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [4(x2- 1)3 + 8x(x2-1)4] / [16(x2-1)3]

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Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. (N ∪ R) ∩ M

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