Will do!
A few things to note about this problem... : 3x^2 - 2x - 5
The coefficient in front of x^2 (3) can only be expressed as 3, thus the start of the factor will look like this:
(3x...
The constant (-5) is negative so that means the two numbers which we choose must be a negative and a positive. Meaning two possible sign orientations are as followed: (The _ are blanks)
(3x - _)(x + _)
(3x + _)(x - _)
The x on the second factor is need to make 3x^2. Now to keep going we need two numbers that multiplied together equal -5.
The only numbers that make sense are ±1, and ±5.
Now we have to somehow arrange it so that one of the two multiplied by 3 and added to the other equals -2.
Let's see our options:
3(-5), 1
5, 3(-1)
3(5), -1
-5, 3(1)
Let's try each of these out. If they work then they'll equal -2.
3(-5) + 1 = -15 + 1 = -14
NOPE!
5 + 3(-1) = 5 - 3 = 2
NOPE! Close though!
3(5) - 1 = 15 - 1 = 14
NOPE!
-5 + 3(1) = -5 + 3 = -2
Checks out!
So now we plug it in!
Remember the 5 needs to be negative, and 1 has to be multiplied by 3 (It has to be in the second factor... below is what I mean)
(3x - 5)(x + 1)
Let's check it by multiplying it all out again.
3x*x + 3x*1 - 5x - 5
3x^2 + 3x - 5x - 5
3x^2 - 2x - 5
Checks out. Hope this helped!