For the following exercises, solve the quadratic equation by factoring. 2 a^2-14 a=0

Name: Problem 87, Chapter 4: Intermediate Algebra
Uploaded: 2020-06-29T17:53:25-08:00
Duration: 2 min 4 s
Channel: Jason Taylor-Pestell
Description: For the following exercises, solve the quadratic equation by factoring. 2 a^2-14 a=0

step 1 All right, so in this problem, we are going to begin by moving terms around to make sure that th

For the following exercises, solve the quadratic equation by...

Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically taking the form ax² + bx + c = 0. They appear in many areas of mathematics and can be solved using various methods including factoring, completing the square, and the quadratic formula. Understanding the properties of quadratic equations is essential for handling problems in algebra and calculus.

Factoring

Factoring is the process of rewriting an algebraic expression as a product of its simpler components or factors. In the context of quadratic equations, factoring involves expressing the quadratic polynomial as a product of two binomials. This method is efficient when the quadratic can be easily decomposed into factors that multiply to give the original expression.

Common Factor Extraction

Common factor extraction is a basic factoring technique where a common factor present in all terms of an expression is identified and factored out. This simplifies the equation and can reduce complex expressions to simpler forms. For quadratic equations, pulling out the greatest common factor can be the first step in further factoring the expression into a product of factors.

Zero Product Property

The zero product property states that if the product of two or more factors is zero, then at least one of the factors must be zero. This is a crucial step when solving factored equations, including quadratic ones, as it allows the equation to be broken down into simpler linear equations. By setting each factor equal to zero, you can solve for the variable.

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