How do you factor the expression #14x^3 - 21x^2 - 2x + 3#?
1 Answer
Dec 29, 2015
Factor by grouping then using the difference of squares identity to find:
#14x^3-21x^2-2x+3#
#=(7x^2-1)(2x-3)#
#=(sqrt(7)x-1)(sqrt(7)x+1)(2x-3)#
Explanation:
The difference of squares identity can be written:
#a^2-b^2 = (a-b)(a+b)#
Use this with
#14x^3-21x^2-2x+3#
#=(14x^3-21x^2)-(2x-3)#
#=7x^2(2x-3)-1(2x-3)#
#=(7x^2-1)(2x-3)#
#=((sqrt(7)x)^2-1^2)(2x-3)#
#=(sqrt(7)x-1)(sqrt(7)x+1)(2x-3)#
