Answer:
g(x) is a factor of P(x).
Step-by-step explanation:
By the factor theorem, If g(a) = 0 and P(a) = 0, then g(x) is a factor of P(x).
Here
P(x) = 2x^3-11x^2-4x+1
g(x) = 2x + 1, g(-1/2) = 0
check
P(-1/2)
= 2(-1/2)^3-11(-1/2)^2-4(-1/2)x+1
=-1/4 - 11/4 + 2 + 1
= 0
Therefore g(x) is a factor of P(x).
As a matter of fact,
P(x) = ( 2x + 1 )( x^2 - 6x + 1 )
