Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
One example of a quadratic equation that can be solved by factoring is:
x^2 + 5x + 6 = 0
To solve this equation by factoring, we first need to factor the quadratic expression on the left side.
(x + 3)(x + 2) = 0
Now, we set each factor equal to zero and solve for x:
x + 3 = 0
x = -3
x + 2 = 0
x = -2
Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -3 and x = -2.
When determining which method to use when solving a quadratic equation, it is important to consider the form of the equation and the available techniques. Factoring is a useful method when the quadratic equation can be easily factored into linear factors. If factoring is not feasible, other methods such as completing the square or using the quadratic formula should be considered. Additionally, the complexity of the equation and personal preference may also impact the choice of method for solving a quadratic equation.