What is the polynomial f(x)=x^3+2x^2-6x-9 divided by x-2

Question

a) What is the polynomial f(x)=x^3+2x^2-6x-9 divided by x-2?

b) What is f(2)

Answer 1

If we divide the coefficients of f(x) by the possible root, 2, we get a quotient with remainder.  The remainder is the value of f(2).

 

2 | 1     2       -6       -9

 

            2        8        4

______________________

     1     4        2       -5

 

 

f(2) = -5

 

 

As for part a)

 

x² + 4x + 2 - (5 / (x - 2))