Question 37023: Factorization of c^3-64.
Answer by jcmtnez(53)   (Show Source):
You can put this solution on YOUR website! You may see that 8^2=64 and therefore (4*2)^2=64, that means that 4^2*2^2=64 (As probably now 2^2=4) therefore 4^2*4=64 that is the same that 4^3=64.
As I show you 4 is a root of the polynomial c^3-64, and therefore when we divide by c-4 we will obtain another polynomial, at this time of degree two.
Using syntethetic division we easily have that (c^3-64)/(c-4)= c^2+4c+16, then we can express c^3-64 as (c-4)(c^2+4c+16) which is the factorized form.
Note: We can make more factorization because the solutions and the factors of c^2+4c+16 involve complex numbers. If you need more help, or you didn't understand something, please ask me again.
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