Answer:
(x + 3)(5x^2 - 2)
Explanation:
To factor the expression 5x^3 + 15x^2 - 2x - 6 using the grouping method, we can follow these steps:
Step 1: Group the terms in pairs:
(5x^3 + 15x^2) + (-2x - 6)
Step 2: Factor out the greatest common factor from each pair:
Finding the greatest common factor (GCF) of (5x^3 + 15x^2):
The GCF of 5x^3 and 15x^2 is 5x^2.
Thus, we have 5x^2(x + 3)
Finding the GCF of (-2x - 6):
The GCF of -2x and -6 is -2:
Thus, we have -2(x + 3)
Combining our two terms gives us 5x^2(x + 3) - 2(x + 3)
Step 3: Notice that (x + 3) is a common factor in both terms. We can factor it out:
(x + 3)(5x^2 - 2)
So, the factored form of the expression 5x^3 + 15x^2 - 2x - 6 using the grouping method is (x + 3)(5x^2 - 2).