How do you factor the expression 14x^3 - 21x^2 - 2x + 314x3−21x2−2x+3?
1 Answer
Dec 29, 2015
Factor by grouping then using the difference of squares identity to find:
14x^3-21x^2-2x+314x3−21x2−2x+3
=(7x^2-1)(2x-3)=(7x2−1)(2x−3)
=(sqrt(7)x-1)(sqrt(7)x+1)(2x-3)=(√7x−1)(√7x+1)(2x−3)
Explanation:
The difference of squares identity can be written:
a^2-b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
Use this with
14x^3-21x^2-2x+314x3−21x2−2x+3
=(14x^3-21x^2)-(2x-3)=(14x3−21x2)−(2x−3)
=7x^2(2x-3)-1(2x-3)=7x2(2x−3)−1(2x−3)
=(7x^2-1)(2x-3)=(7x2−1)(2x−3)
=((sqrt(7)x)^2-1^2)(2x-3)=((√7x)2−12)(2x−3)
=(sqrt(7)x-1)(sqrt(7)x+1)(2x-3)=(√7x−1)(√7x+1)(2x−3)
