Question

Use synthetic division to find the quotient and the remainder for the problem: (12x^4 + 5^3 + 3x^2 - 5)/(x+1)?,

Answer 1

Step 1 : Setting up the problem

Write the coefficients of the dividend in the same order. For missing terms, enter the co-efficient as zero. Set the divisor equal to zero and use that number in the division box.

The problem now looks as follows:

 -1 | 12 5 3 0 -5

Step 2 : Bring down the first co-efficient and write it in the bottom row.

 -1 | 12 5 3 0 -5
 ______________________ 12 

Step 3 : Multiply the first coefficient with the divisor and enter the value below
the next co-efficient. Add the two and write the value in the bottom row.

 -1 | 12 5 3 0 -5
 _____-12_______________ 12 -7

Step 4 : Repeat Step 3 for rest of the coefficients as well:

 -1 | 12 5 3 0 -5
 ____________7 ___________ 12 -7 10 


 -1 | 12 5 3 0 -5 ______________ -10______ 12 -7 10 -10 
  -1 | 12 5 3 0 -5 ____________________ 10_ 12 -7 10 -10 5 
 The last row now represents the quotient coefficients and the remainder. Co-efficients of Quotient are written one power less than their original power and the remainder is written as a fraction.

Answer :12x^3-7x^2+10x-10+5/(x+1) where the last term denotes the remainder and the rest is the quotient.