. Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
2. 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?
Equation:
x^2 + 5x + 6 = 0
To solve this equation by factoring, we need to find two numbers that multiply to 6 and add up to 5 (the coefficient of the x term). 2 and 3 fit these criteria, so we can rewrite the equation as:
(x + 2)(x + 3) = 0
Now we can set each factor equal to zero and solve for x:
x + 2 = 0
x = -2
x + 3 = 0
x = -3
Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.
When determining which method to use to solve a quadratic equation, it is helpful to consider the form of the equation and the tools you have available. If the equation can be easily factored, as in the case above, factoring is typically the quickest method. If factoring is not feasible, you can also try using the quadratic formula or completing the square to solve the equation. It may take some trial and error to determine which method will be most efficient in each specific case.