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 <span>±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 </span>-5, 3(1) <span> 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)
