1. solve this x²+5x+4=0 quadratic equation that can be solved by factoring. Solve your equation and show your work.
To solve the quadratic equation x² + 5x + 4 = 0 by factoring, we need to find two numbers that multiply to 4 and add up to 5.
The two numbers are 1 and 4, because 1 * 4 = 4 and 1 + 4 = 5.
So, we rewrite the equation as:
x² + 1x + 4x + 4 = 0
Now, we can factor by grouping:
x(x + 1) + 4(x + 1) = 0
(x + 1)(x + 4) = 0
Now, we can set each parenthesis equal to zero:
x + 1 = 0 or x + 4 = 0
x = -1 or x = -4
Therefore, the solutions to the equation x² + 5x + 4 = 0 are x = -1 and x = -4.