Question

Match each step with the correct expression to factor 20x² - 25x - 30 by using the decomposition method.

Answer 1

To factor 20x² - 25x - 30 using the decomposition method, follow these step-by-step instructions.

Step-by-step explanation:

To factor the quadratic expression 20x² - 25x - 30 using the decomposition method, you need to follow these steps:

1. Find the product of the coefficient of x² (20) and the constant term (-30). In this case, 20 * -30 = -600.
2. Find two numbers whose product is -600 and whose sum is the coefficient of the x term (-25). In this case, the numbers are -40 and 15 (-40 * 15 = -600 and -40 + 15 = -25).
3. Split the middle term (-25x) into -40x and 15x, using the numbers found in the previous step.
4. Factor by grouping. Group the terms: 20x² - 40x + 15x - 30.
5. Factor out the greatest common factor from each group: 20x(x - 2) + 15(x - 2).
6. Factor out the common binomial factor: (x - 2)(20x + 15).