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

1 Answer
Dec 28, 2015

Answer:

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)#