Final answer:
To factor the expression 20x²+25x-30 using the decomposition method, you need to find two numbers that multiply to give the product of the coefficient of the x² term and the constant term, and add up to give the coefficient of the x term. Then, group the terms and factor out the common binomial.
Step-by-step explanation:
To factor the expression 20x²+25x-30 using the decomposition method, we need to find two numbers that multiply to give the product of the coefficient of the x² term (20) and the constant term (-30), and add up to give the coefficient of the x term (25).
The numbers that satisfy these conditions are 30 and -1. Therefore, we can rewrite the expression as 20x²+30x-x-30.
Next, we group the terms:
20x²+30x-x-30 = (20x²+30x) + (-x-30).
Now, we can factor out the greatest common factor from each group:
20x(x+3) - 1(x+3).
Finally, we can factor out the common binomial (x+3) from both terms:
(20x-1)(x+3).