Synthetic Division: Find Quotient & Remainder of 4x^2 + x / (x + 1)

This guide demonstrates how to find the quotient and remainder when dividing the polynomial 4x^2 + x by (x + 1) using the method of synthetic division. Here's a detailed walkthrough:

Step 1: Setting Up the Synthetic Division Table

Begin by setting up the synthetic division table. Write the coefficients of the dividend (4x^2 + x) in the top row, making sure to include a zero for any missing terms. Then write the divisor (x + 1) in the form '-1' (the opposite of the constant term) on the left side of the table.

 -1 | 4   0   1

Step 2: Bring Down the First Coefficient

Bring down the first coefficient of the dividend (4) into the bottom row.

 -1 | 4   0   1
      |---
      | 4

Step 3: Multiply and Write the Result

Multiply the divisor ('-1') by the number in the bottom row (4) and write the result in the next row.

 -1 | 4   0   1
      |---
      |-4

Step 4: Add the Numbers in the Second Row

Add the numbers in the second row (0 and -4).

 -1 | 4   0   1
      |---
      |-4

Step 5: Multiply and Write the Result (Again)

Multiply the divisor ('-1') by the sum in the second row (-4) and write the result in the next row.

 -1 | 4   -4   1
      |---
      |-4

Step 6: Add the Numbers in the Third Row

Add the numbers in the third row (1 and -4).

 -1 | 4   -4   1
      |---
      |-4
      |-3

Step 7: Interpret the Results

The numbers in the bottom row represent the coefficients of the quotient. The last number (-3) represents the remainder.

Therefore, the quotient is 4 - 4x, and the remainder is -3.

You have now successfully used synthetic division to find the quotient and remainder for 4x^2 + x divided by (x + 1). This method is a quick and efficient way to perform polynomial division.