Question

Using factor theorem determine whether g(x) is a factor of p(x)

Answer 1

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 )