Question

please solve this problem as early as possible. ​

Answer 1

Step-by-step explanation:

(i)g(x)=2

g(x) will be factor of f(x) if f(2)=0

f(x)=2(x)^3-11(x)²+17x-6

f(2)=2*(2)^3-11*(2)²+17*2-6

    =2*8-11*4+34-6

    =16-44+34-6

    =50-50

    =0

therefore g(2) is factor of f(x)

(ii) g(x)=3

g(x) will be factor of f(x) if f(3)=0

Now,

f(3)=2*(3)^3-11*(3)²+17*3-6

    =2*27-11*9+51-6

    =54-99+51-6

    =105-105

    =0

therefore, g(x) is factor of f(x).

(iii) g(x)=1/2

g(x) will be factor of f(x) if f(1/2)=0

Now,

f(1/2)=2*(1/2)^3-11*(1/2)²+17*1/2-6

       =2*1/8-11*1/4+17/2-6

       =1/4-11/4+17/2-6

       =1-11+34-64

       =35-17/4

       =18/4

       =9/2

therefore, g(x) is not factor of f(x) ans

I hope it helps you

Plz...... mark Brainliest