1. Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
One possible quadratic equation that can be solved by factoring is:
x^2 + 6x + 8 = 0
To solve this equation, we can look for two numbers that multiply to 8 and add to 6. These numbers are 2 and 4, so we can rewrite the equation as:
x^2 + 2x + 4x + 8 = 0
Now we can group the terms and factor by grouping:
(x^2 + 2x) + (4x + 8) = 0
x(x + 2) + 4(x + 2) = 0
(x + 2)(x + 4) = 0
Therefore, the solutions of the equation are x = -2 and x = -4.
Explanation: The quadratic equation x^2 + 6x + 8 = 0 can be solved by factoring because it has integer coefficients and a constant term that is the product of the leading coefficient and the constant term. To solve the equation, we need to find two numbers that add up to the coefficient of the linear term and multiply to the constant term. This is possible in this case because 6 can be written as the sum of 2 and 4, which are the factors of 8. By grouping and factoring, we can then rewrite the equation as the product of two linear factors, which gives us the solutions of the equation.