Question

on dividing x^3-6x^2+11x-6 by a polunomial g(x), the quotient and the remainder were c^2-8x+27 and -60 respectively.Find g(x)

Answer 1

Answer:

Step-by-step explanation:

If we divide f(x)=3x  

3

+x  

2

+2x+5 by g(x) we get q(x)=(3x−5) as quotient and r(x)=(9x+10) as remainder.

By using division algorithm,

f(x)=g(x)q(x)+r(x)

⟹3x  

3

+x  

2

+2x+5=g(x)(3x−5)+(9x+10)

⟹g(x)=  

(3x−5)

3x  

3

+x  

2

+2x+5−9x−10

​  

 

⟹g(x)=  

(3x−5)

3x  

3

+x  

2

−7x−5

​  

 

Hence, g(x)=x  

2

+2x+1