Question

Some steps to rewrite the expression x3 − x + 2x2 − 2 as a product of three factors are shown below:
Step 1: x3 − x + 2x2 − 2
Step 2: x3 + 2x2 − x − 2
Step 3: x2(x + 2) − 1(x + 2)
Which of the following best shows the next two steps to rewrite the expression? Step 4: (x2 + 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)
Step 4: (x2 − 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 2)
Step 4: (x2 − 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)
Step 4: (x2 + 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 1)

Answer 1

Your second option is correct.
Once you have the step 3 x2(x+2)-1(x+2)
You can combine the two (x+2)s and connect the x2 with the -1 as so:

(x2-1)(x+2)

Now, (x2-1) can be rewritten as:
(x-1)(x+1)

So total, for step 5:
(x-1)(x+1)(x+2)

I hope this Helps!