How do you factor the expression #14x^3 - 21x^2 - 2x + 3#?

1 Answer
Dec 29, 2015

Answer:

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 #a=sqrt(7)x# and #b=1# to find:

#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)#