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Ch. 1 - Equations and Inequalities
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 1 - Equations and InequalitiesProblem 14
Chapter 2, Problem 14

Solve each equation using the zero-factor property. x2 + 2x - 8 = 0

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Start with the given quadratic equation: \(x^{2} + 2x - 8 = 0\).
Factor the quadratic expression on the left side. Look for two numbers that multiply to \(-8\) and add to \(2\).
Write the factored form as a product of two binomials: \((x + a)(x + b) = 0\), where \(a\) and \(b\) are the numbers found in the previous step.
Apply the zero-factor property, which states that if \(AB = 0\), then either \(A = 0\) or \(B = 0\). Set each binomial equal to zero: \(x + a = 0\) and \(x + b = 0\).
Solve each equation for \(x\) to find the solutions to the original quadratic equation.

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Key Concepts

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

Zero-Factor Property

The zero-factor property states that if the product of two factors equals zero, then at least one of the factors must be zero. This property is essential for solving quadratic equations that are factored into binomials, allowing us to set each factor equal to zero and solve for the variable.
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Factoring Quadratic Equations

Factoring involves rewriting a quadratic equation as a product of two binomials. For example, x² + 2x - 8 can be factored into (x + 4)(x - 2). This step is crucial because it prepares the equation for applying the zero-factor property to find the solutions.
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Solving Quadratic Equations

Solving quadratic equations means finding the values of the variable that satisfy the equation. After factoring and applying the zero-factor property, you solve the resulting simple linear equations to find the roots or solutions of the original quadratic.
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Related Practice
Textbook Question

Solve each equation. 6(3x-1)= 8 - (10x-14)

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Textbook Question

Solve each equation. 56x−2x+43=53\(\frac{5}{6}\)x - 2x + \(\frac{4}{3}\) = \(\frac{5}{3}\)

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Solve each equation using the zero-factor property. x2 - 5x + 6 = 0

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Solve each equation. | (x - 4)/ 2| = 5

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Textbook Question

Solve each problem. See Example 1. The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width.

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Textbook Question

Use the following facts. If x represents an integer, then x+1 represents the next consecutive integer. If x represents an even integer, then x+2 represents the next consecutive even integer. If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive odd integers whose product is 143.