Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the zero-factor property? Solve it

Key Concepts

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 is essential for solving polynomial equations that can be factored into simpler linear expressions. For example, if (a)(b) = 0, then either a = 0 or b = 0, allowing us to find the values of x that satisfy the equation.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors, which can simplify solving equations. For instance, the equation (3x - 1)(x - 7) = 0 is already factored, making it straightforward to apply the Zero-Product Property. Understanding how to factor different types of polynomials is crucial for identifying equations suitable for this method.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. They can be solved using various methods, including factoring, completing the square, or the quadratic formula. Recognizing a quadratic equation allows students to determine the best approach for finding its roots, especially when it can be factored easily.