math,correction

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Is this correct or no. I need help in a couple of problems can someone explain them to me.

Problem#1
directions: Factor each expression

a^2(b-c)-16b^2(b-c)

My answer is:

(b-c)(a-4b)(a+4b)


PROBLEM#2
dIRECTIONS: Find a value for k so that 2x^3-kxy^2 will have the facotors 2x,x-3y,and x+3y

MY steps:
=2x(x-3y)(x+3y)
=2x(x^2-9y^2)
=2x^3-18xy^2

so, k = 18

Problem#3
Directions: Factor each polynomial by grouping the first two terms and the last two terms.

x^3-4x^2+2x-8

MY answer:
(x-4)(x^2+2)


Looks OK!

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