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

Remainder = zero

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

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