Question

How do you factor `x^3+3x^2-x-3=0`?

Answer 1

Alternatively, you can factor by grouping and using the difference of squares identity to find:

`x^3+3x^2-x-3=(x-1)(x+1)(x+3)`

Explanation:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

Factor by grouping then using the difference of squares identity with `a=x` and `b=1` as follows:

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

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

`=x^2(x+3)-1(x+3)`

`=(x^2-1)(x+3)`

`=(x^2-1^2)(x+3)`

`=(x-1)(x+1)(x+3)`