Question

Has the polynomial been factored correctly?

x^5-16x^3+8x^2-128
x^3(x^2-16)+8(x^2-16)
(x^2-16)(x^3+8)

If not explain why please

Answer 1

wrong by try 8x^2 =! -16x^2

Answer 2

(x^2 - 16) is x^2 - 4^2 that can be factored further.
Use the identity: a^2 - b^2 = (a+b)(a-b)

And x^3 + 8 = x^3 + 2^3 which can also be factored further.
Use the identity: a^3 + b^3 = (a+b)(a^2 - ab + b^2)