Question

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

Answer 1

(x + 3 )(x + 1 )(x - 1 )

Explanation:

Factorise by grouping.

ie `[ x^3 + 3x^2 ] + [ - x - 3 ]`

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

[common factor of ( x + 3 ) ]

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

`(x^2 - 1 ) =(x + 1 )(x - 1 ) color(black)(" difference of 2 squares ")`

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