Question

Some steps to rewrite the expression x^3 - x + 2x^2 - 2 as a product of three factors are shown below:

Step 1: x^3 - x + 2x^2 - 2
Step 2: x^3 + 2x^2 - x - 2
Step 3: x^2(x + 2) - 1(x + 2)

Which of the following best shows the next two steps to rewrite the expression?

Step 4: (x^2 + 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)

Step 4: (x^2 - 1)(x + 2); Step 5: (x - 1)(x + 1)(x + 2)

Step 4: (x^2 - 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)

Step 4: (x^2 + 1)(x + 2); Step 5: (x - 1)(x + 1)(x + 2)

Answer 1

They're factoring by grouping. If you know how to do it using that method, you should be able to figure out what comes next..

Answer 2

Step 4: (x^2 - 1)(x + 2); Step 5: (x - 1)(x + 1)(x + 2)

How?
After step 3.

Factor the polynomial by grouping the first two terms together and finding the greatest common factor (GCF). Next, group the second two terms together and find the GCF. Since both groups contain the factor they can be combined.

Answer 3

x^3+2 x^2-x-2
Factor pairs of terms in x^3+2 x^2-x-2 by grouping.
Factor terms by grouping. x^3+2 x^2-x-2 = (x^3+2 x^2)+(-2-x) = x^2 (x+2)-(x+2):
x^2 (x+2)-(x+2)
Factor common terms from x^2 (x+2)-(x+2).
Factor x+2 from x^2 (x+2)-(x+2):
(x+2) (x^2-1)
Write 1 as a square in order to express x^2-1 as a difference of squares.
x^2-1 = x^2-1^2:
(x+2) (x^2-1^2)
Factor the difference of two squares.
Factor the difference of two squares. x^2-1^2 = (x-1) (x+1):
then u ll get
| (x-1) (x+1) (x+2)

Answer 4

i really don't know i am just here to help people but i am getting a message saying the am trying to violate the rules by giving the answers