Solve each equation using the zero-factor property. See Example 1. -6x^2 + 7x = -10

Key Concepts

Zero-Factor Property

The Zero-Factor Property states that if the product of two or more factors equals zero, then at least one of the factors must be zero. This principle is essential for solving polynomial equations, as it allows us to set each factor equal to zero to find the solutions of the equation.

Quadratic Equations

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. In the given equation, -6x^2 + 7x + 10 = 0 is a quadratic equation that can be solved using the zero-factor property after rearranging it into standard form.

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of its factors. For quadratic equations, this often means rewriting the equation in a form like (px + q)(rx + s) = 0, which can then be solved using the zero-factor property. Mastery of factoring is crucial for efficiently solving quadratic equations.