Divide (x^3-x^2-2x+6)/(x-2)

Problem

(x^3−x^2−2*x+6)/(x−2)

Solution

1. Set up the synthetic division using the root of the divisor x−2 which is 2 and the coefficients of the dividend $1, -1, -2, 6$.

2. Bring down the first coefficient, 1

3. Multiply the root 2 by the value just written 1 to get 2 and add it to the next coefficient −1 to get 1

4. Multiply the root 2 by the new value 1 to get 2 and add it to the next coefficient −2 to get 0

5. Multiply the root 2 by the new value 0 to get 0 and add it to the last coefficient 6 to get the remainder 6

6. Interpret the resulting coefficients $1, 1, 0a*s(t)*h*e*q*u*o*t*i*e*n*t^2 + x + 0a*n*d(t)*h*e*r*e*m*a*i*n*d(e)*ro*v*e*r*t*h*e*d(i)*v*i*s(o)*r - 2$.

Final Answer

(x^3−x^2−2*x+6)/(x−2)=x^2+x+6/(x−2)

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