Need help with factoring a few quadratic problems. Thanks!

Question

1. Solve 6x² +5x - 4 = 0 by factoring. Enter each step.

2. When solving an equation set equal to zero by graphing, why are the x-intercepts the solutions to the equation? Create an example equation to help you explain.

Answer 1

1. Solve 6x² + 5x - 4 = 0 by factoring. Enter each step.

Step 1) List all factors of 6 and 4:

6: 1 and 6, 2 and 3

4: 1 and 4, 2 and 2

Step 2) Determine which set of factors will add up to 5:

(2x - 1)(3x + 4) = 0

Step 3) Set each factor equal to 0 to find the zeros:

2x - 1 = 0 => x = 1/2

3x + 4 = 0 => x = -4/3

2. When solving an equation set equal to zero by graphing, why are the x-intercepts the solutions to the equation? Create an example equation to help you explain.

If either factor is equal to zero, anything multiplied by zero will equal zero, so y will equal zero at that x-value and the polynomial will cross the x-axis.

For example, let's take the equation y = x² + x - 2. If we factor it out and set it to zero we get y = (x + 2)(x - 1) = 0. Solving for the zeros we get x = -2 and x = 1. If we look at the point x = -2, y = (-2 + 2)(-2 - 1) = (0)(-3) = 0. If we look at the point x = 1, y = (1 + 2)(1 - 1) = (3)(0) = 0. Notice that if either factor equals zero, the whole equation will equal zero.