Question

What is the result when 4x^4-11x^3-24x^2+19x-124x 4 −11x 3 −24x 2 +19x−12 is divided by x-4x−4? If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+ b(x) r(x) ​ .

Answer 1

Answer:

Remainder = zero

Answer = (4x^3)  +(5x^2) -4x +3  or 4x³ +5x²-4x+3

Step-by-step explanation:

        (4x^3)  +(5x^2) -4x +3        

x-4√4x^4-11x^3-24x^2+19x-12               We multiply (x-4) by  4x³      

        4x^4-16x^3

       -          +          

                5x^3-24x^2+19x-12

                 5x^3-20x^2                          We multiply (x-4) by  +5x²    

                -          +        

                        -4x^2+19x-12

                         -4x^2+16x                          We multiply (x-4) by - 4x

                         +         -            

                                    3x-12

                                     3x-12                      We multiply (x-4) by +3

                                  -       +          

                                 zero remainder

We keep multiplying the factor  (x-4)  by different terms to get the first term desired in each step . Then we subtract by changing the signs and get the remainder.

The answer is the expression obtained at the top.

4x^4-11x^3-24x^2+19x-124 /x-4 = 4x³ +5x²-4x+3