use the grouping method to factor 2x^3+6x^2-7x-21

Answer 1

First, we group the terms in pairs:

2x^3 + 6x^2 - 7x - 21
= (2x^3 + 6x^2) + (-7x - 21)
= 2x^2(x + 3) - 7(x + 3)

Now, we can see that both terms have a common factor of (x + 3), so we factor that out:

= (2x^2 - 7)(x + 3)

Therefore, the factored form of 2x^3 + 6x^2 - 7x - 21 is (2x^2 - 7)(x + 3).