Answer:
(3x-1)(x+1)
Explanation:
I like to factor by grouping.
a=3
b=2
c=-1
To get those values I compared 3x^2+2x-1 to ax^2+bx+c.
Now our objective to help us factor this is: Find two integers that multiply to be a*c and add up to be b.
a*c=3(-1)
b=2
Guess what? Our numbers are already visible to us; that doesn't always happen. However, a*c=3(-1) and b=2=3+(-1).
So we are going to replace our 2x with 3x+-1x or -1x+3x. Either one is fine; they are the same thing.
3x^2+2x-1
Replacing 2x with -1x+3x.
3x^2-1x+3x-1
Grouping first 2 terms together and grouping 2nd 2 terms together.
(3x^2-1x)+(3x-1)
Now we are going to factor each grouping.
x(3x-1)+1(3x-1)
Now notice we have two terms here x(3x-1) and 1(3x-1). Both of these terms have a common factor of (3x-1). We are going to now factor out (3x-1).
(3x-1)(x+1)