Solving Quadratic Equations by Factoring
Solve quadratic equations by factoring in Grade 9 algebra: set the equation equal to zero, factor the trinomial, then apply the Zero Product Property to find both solutions.
Key Concepts
New Concept If the product of two quantities equals zero, at least one of the quantities equals zero. What’s next Next, you’ll use this property to factor and find the roots of several quadratic equations, including real world application problems.
Common Questions
What are the steps to solve a quadratic equation by factoring?
First, set the equation equal to zero. Then factor the quadratic expression. Finally, set each factor equal to zero and solve for the variable. For x² - 5x + 6 = 0, factor to (x-2)(x-3) = 0, giving x = 2 or x = 3.
What is the Zero Product Property and why is it key to factoring?
The Zero Product Property states that if a × b = 0, then a = 0 or b = 0. After factoring a quadratic into two factors, setting each equal to zero gives the two solutions.
What quadratics can be solved by factoring?
Quadratics with integer solutions are best solved by factoring. Look for two numbers that multiply to the constant term c and add to the coefficient b. Not all quadratics factor over integers — those require completing the square or the quadratic formula.