Question

Solve using the zero-factor property. $$ x^{2}-x-56=0 $$

   Solve using the zero-factor property.
$$
x^{2}-x-56=0
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 11, Problem 9

Instant Answer

Solved by Expert Nick Johnson

02/10/2022

Step 1

We are looking for two numbers that multiply to -56 and add to -1. The numbers that satisfy this are -8 and 7. So, we can write the equation as: $$ x^{2}-x-56=(x-8)(x+7)=0 $$ Show more…

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Solve using the zero-factor property. $$ x^{2}-x-56=0 $$

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Key Concepts

Factoring Method

Factoring is a method of rewriting a quadratic equation as a product of two binomials. This approach involves finding two numbers that multiply to the constant term, c, and add to the coefficient, b, of the x term. Once factored, the equation is set to zero, allowing for the application of additional properties to find the solutions.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants and a ? 0. These equations are foundational in algebra and can be solved by various methods including factoring, completing the square, and using the quadratic formula.

Zero Product Property

The zero product property, also known as the zero-factor property, states that if the product of two expressions is equal to zero, then at least one of the expressions must be zero. This principle is crucial when solving quadratic equations by factoring, as it enables the separation of the equation into individual factors that can each be set equal to zero to find the variable's solutions.

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