How do you factor #h(x)=x^3-3x^2-x+3#?
1 Answer
Dec 19, 2015
Factor by grouping then using the difference of squares identity to find:
#x^3-3x^2-x+3 =0 =(x-1)(x+1)(x-3)#
Explanation:
The difference of squares identity may be written:
#a^2-b^2 = (a-b)(a+b)#
After factoring by grouping use this identity with
#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)#
