Express f(x) in the form f(x)= (x-k)q(x) +r for the given value of k.

Question

Express f(x) in the form f(x)= (x-k)q(x) +r for the given value of k.

 

F(x)=3x^3+x^2+x-4, k=-1

 

f(x)=?

Answer 1

f(x) = 3x^3 + x^2 + x - 4

 

-1 | 3  1 1   -4

         -3 2   -3        

      3 -2 3 | -7

 

f(x) =(x + 1)(3x^2 - 2x + 3) - 7

 

check:

 

(x + 1)(3x^2 - 2x + 3) - 7 =? 3x^3 + x^2 + x - 4

 

x(3x^2 - 2x + 3)

+1(3x^2 - 2x + 3) - 7 =? 3x^3 + x^2 + x - 4

 

3x^3 - 2x^2 + 3x

        + 3x^2 - 2x + 3 - 7 =? 3x^3 + x^2 + x - 4

3x^3 + x^2 + x - 4 = 3x^3 + x^2 + x - 4   √