Answer:
The correct option is c.
Step-by-step explanation:
The dividend is
[tex]x^3+1[/tex]
It can be rewritten as
[tex]x^3+0x^2+0x+1[/tex]
Therefore the coefficient of dividend are 1,0,0 and 1.
The divisor is (x-1). The divisor in the form of (x-c), therefore the value of c is 1.
Write the coefficient and value of c in top row.
Write the first coefficient in bottom row.
Multiply 1 by 1 and write the result below the second coefficient in the middle row, then add them.
After that multiply 1 by resulting 1 and write the result below the third coefficient in the middle row, then add them.
Apply same processes till the end.
The bottom row represents the coefficient of quotient and remainder.
From the below figure we can say that the coefficient of quotient are 1,1,1 and the remainder is 2.
The degree of the quotient is 1 less than the degree of dividend. Therefore degree of quotient is 2.
[tex]\frac{x^3+1}{x-1}=x^2+x+1+\frac{2}{x-1}[/tex]
Option c is correct.
