C. x³-4x²-16x+24.
In order to solve this problem we have to use the product of the polynomials where each monomial of the first polynomial is multiplied by all the monomials that form the second polynomial. Afterwards, the similar monomials are added or subtracted.
Multiply the polynomials (x-6)(x²+2x-4)
Multiply eac monomial of the first polynomial by all the monimials of the second polynomial:
(x)(x²)+x(2x)-(x)(4) - (6)(x²) - (6)(2x) - (6)(-4)
x³+2x²-4x -6x²-12x+24
Ordering the similar monomials:
x³+(2x²-6x²)+(-4x - 12x)+24
Getting as result:
x³-4x²-16x+24