How do you factor: y= x^6 - 16x^3 +64x ?

1 Answer
Apr 20, 2016

y=(x-2)^2(x+1+isqrt 3))^2(x+1-isqrt3))^2

Explanation:

y is a quadratic that is perfect square.

Factorizing this quadratic and using (a^3-b^3)=(a-b)(a^2+ab+b^2),

y=(x^3-2^3)^2=((x-2)(x^2+2x+4))^2

=(x-2)^2((x+1)^2+(sqrt 3)^2)^2

=(x-2)^2(x+1+isqrt 3))^2(x+1-isqrt3))^2