SAT Level 5 Passport to Advanced Math Problem

Here is a difficult Passport to Advanced Math problem for the SAT. I will provide a solution soon.

Level 5 Passport to Advanced Math

g(x)=x2 + 4x 1
h(x)=2x3 + 3x2 + x

The polynomials g and h are defined above. Which of the following polynomials is divisible by 2x 1 ?

A) k(x) = g(x) h(x)
B) k(x) = 12g(x) h(x)
C) k(x) = g(x) 10h(x)
D) k(x) = 12g(x) 10h(x)

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