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

it seems like the  answer would be 1 then 0

Answer 2

Answer:  The complete factorization is  (x - 1)(x + 1)(x + 2).

Step-by-step explanation:  We are given to complete the factorization of the following polynomial:

$P=x^3+2x^2-x-2.$

Let us try to factorize the given polynomial.

We have

$P\\\\=x^3+2x^2-x-2\\\\=x^2(x-1)+3x(x-1)+2(x-1)\\\\=(x-1)(x^2+3x+2)\\\\=(x-1)(x^2+2x+x+2)\\\\=(x-1)\{x(x+2)+1(x+2)\}\\\\=(x-1)(x+1)(x+2).$

Thus, the required complete factorization of the polynomials with numbers in the ascending order is (x - 1)(x + 1)(x + 2).