Question

Solve using the zero-factor property. $$ x^{2}=121 $$

   Solve using the zero-factor property.
$$
x^{2}=121
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 11, Problem 13

Instant Answer

Solved by Expert Nick Johnson

02/10/2022

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Solve using the zero-factor property. $$ x^{2}=121 $$

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Key Concepts

Quadratic Equations in Standard Form

Quadratic equations are often expressed in standard form as ax^2 + bx + c = 0. Converting a quadratic equation to this standard form is a key step before applying factoring techniques or other solution methods. Once in standard form, the equation can be analyzed for factorability and solved by methods such as factoring, completing the square, or using the quadratic formula.

Zero-Factor Property

The zero-factor property states that if a product of two or more factors is equal to zero, then at least one of the factors must be zero. This property is essential for solving equations that can be factored, as it allows us to set each factor equal to zero and solve for the variable, thereby breaking down a complex equation into simpler linear equations.

Factoring Difference of Squares

Recognizing and factoring a difference of squares is a valuable algebraic technique. A difference of squares is an expression formed by subtracting one perfect square from another and can be factored into the product of two binomials. This approach is particularly useful for solving equations where the structure matches the form a^2 - b^2, as it simplifies the problem and sets up the use of the zero-factor property.

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