Question

Fill in the missing numbers to complete the factorization. Some of the numbers could be negative. Type the numbers in increasing order.

x 3 + 2x 2 - x - 2 = (x +______________ )(x + ______________)(x +_______________ )

Answer 1

(x-1)(x+1)(x+2)

Explanation:

Lets use grouping method to factor

`x^3+2x^2-x-2`

We group first two terms and last two terms

`(x^3+2x^2)+(-x-2)`

Factor out GCf from each group

GCf for first group is x^2 and for second group is -1

`x^2(x+2)-1(x+2)`

We have x+2 in common , so we factor out x+2

`(x^2-1) (x+2)`

Now we factor x^2 -1

We use difference of squares formula a^2-b^2 = (a+b)(a-b)

x^2 -1 can be written as x^2 - 1^2

`x^2 - 1^2 = (x+1)(x-1)`

So factors are (x+1)(x-1)(x+2)

We write it in increasing order

(x-1)(x+1)(x+2)