1. Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
with 3
as the coefficient of x^2:
The quadratic equation that can be solved by factoring is:
3x^2 + 7x + 2 = 0
To solve this equation using factoring, we need to find two numbers that multiply to 3*2=6 and add to 7. These numbers are 3 and 2.
We can then rewrite the equation as:
3x^2 + 3x + 4x + 2 = 0
Factor by grouping:
(3x+2)(x+1) = 0
Set each factor equal to zero and solve for x:
3x+2=0 or x+1=0
x = -2/3 or x = -1
Therefore, the solutions to the quadratic equation 3x^2 + 7x + 2 = 0 are x = -2/3 and x = -1.