Divide Using Synthetic Division (x^2-6x-6x^3+x^4)/(6+x)

Problem

(x2−6*x−6*x3+x4)÷(6+x)

Solution

1. Rearrange the dividend in descending order of powers to identify the coefficients.

x4−6*x3+x2−6*x+0

2. Identify the coefficients of the dividend and the value of c from the divisor x−c

Coefficients: *1,−6,1,−6,0

Divisor: *x+6⇒c=−6

3. Set up the synthetic division by bringing down the first coefficient.

−6∣1−6*1−6*0

↓

1

4. Multiply the value c by the bottom value and add it to the next coefficient.

−6×1=−6⇒−6+(−6)=−12

−6×(−12)=72⇒1+72=73

−6×73=−438⇒−6+(−438)=−444

−6×(−444)=2664⇒0+2664=2664

5. Interpret the resulting row as the coefficients of the quotient and the remainder.

Quotient coefficients: *1,−12,73,−444

Remainder: *2664

Final Answer

(x4−6*x3+x2−6*x)÷(x+6)=x3−12*x2+73*x−444+2664/(x+6)

Want more problems? Check here!