How do you factor 4c^3-2c^2-6c4c3−2c2−6c?
1 Answer
Aug 30, 2016
Explanation:
Note that all of the terms are divisible by
We can then factor the remaining quadratic by completing the square and using the difference of squares identity:
a^2-b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
with
4c^3-2c^2-6c4c3−2c2−6c
=c(4c^2-2c-6)=c(4c2−2c−6)
=c((2c-1/2)^2-1/4-6)=c((2c−12)2−14−6)
=c((2c-1/2)^2-25/4)=c((2c−12)2−254)
=c((2c-1/2)^2-(5/2)^2)=c((2c−12)2−(52)2)
=c((2c-1/2)-5/2)((2c-1/2)+5/2)=c((2c−12)−52)((2c−12)+52)
=c(2c-3)(2c+2)=c(2c−3)(2c+2)
