Textbook Question
Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = 2x-2
5
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 1
Solve each equation in Exercises 1 - 14 by factoring.
Verified step by step guidance1
Start with the quadratic equation: \(x^2 - 3x - 10 = 0\).
Look for two numbers that multiply to the constant term \(-10\) and add up to the coefficient of the linear term \(-3\).
Express the quadratic as a product of two binomials using those two numbers: \((x + a)(x + b) = 0\), where \(a\) and \(b\) are the numbers found in the previous step.
Set each binomial equal to zero to find the solutions: \(x + a = 0\) and \(x + b = 0\).
Solve each equation for \(x\) to find the roots of the quadratic.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Quadratic Equations
Factoring quadratic equations involves rewriting the quadratic expression as a product of two binomials. This method is useful when the quadratic can be expressed as (x + a)(x + b) = 0, where a and b are numbers that multiply to the constant term and add to the coefficient of the linear term.
Recommended video:
06:08
Solving Quadratic Equations by Factoring
Zero Product Property
The zero product property states that if the product of two factors equals zero, then at least one of the factors must be zero. This property allows us to set each factor equal to zero and solve for the variable, which is essential for finding the roots of the equation after factoring.
Recommended video:
3:49Product, Quotient, and Power Rules of Logs
Solving Quadratic Equations
Solving quadratic equations means finding the values of the variable that satisfy the equation. After factoring, these solutions are found by setting each factor equal to zero and solving the resulting linear equations, yielding the roots or solutions of the quadratic.
Recommended video:
06:08Solving Quadratic Equations by Factoring
Related Practice
Textbook Question
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle.
3
views
Textbook Question
Plot the given point in a rectangular coordinate system. (1, 4)
7
views
Textbook Question
In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 - 4i)
Textbook Question
Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = x^2-3
23
views
1
rank
Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (1, 6]
2
views