Solve each equation in Exercises 1 - 14 by factoring. 3x^2 - 2x = 8

Key Concepts

Factoring Quadratic Equations

Factoring is the process of breaking down a quadratic equation into simpler expressions that can be multiplied to yield the original equation. In the case of a standard quadratic equation in the form ax^2 + bx + c = 0, factoring involves finding two binomials that multiply to give the quadratic. This method is essential for solving equations, as it allows us to set each factor equal to zero and solve for the variable.

Setting the Equation to Zero

To solve an equation by factoring, it is crucial to rearrange the equation so that one side equals zero. This is typically done by moving all terms to one side of the equation. For example, in the equation 3x^2 - 2x - 8 = 0, we isolate the quadratic expression, which allows us to apply the factoring method effectively and find the values of x that satisfy the equation.

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 principle is fundamental when solving factored equations, as it allows us to set each factor equal to zero and solve for the variable. For instance, if we factor the equation into (ax + b)(cx + d) = 0, we can conclude that either ax + b = 0 or cx + d = 0 must hold true.