Dividing Polynomials Using Synthetic Division

Synthetic Division

​Dividing Polynomials

Must be in standard form to divide.

Use place holders for missing powers.​

​Remember: Standard form is in order from highest to lowest power.

Open Ended

Write the following polynomial in standard form:

$$4x^2+7x-3x^3+10x^4-9$$  

​Example of place holders

5x³ + 10x - 5

​We use 0's as a place holder for missing powers.

​Example of synthetic division (pencils down. Just watch me)

2x³ + 5x² + 9 ÷ (x + 3)

​Step by Step

Step 1: Put dividend in standard form

Step 2: Use place holders (if needed)

Step 3: List all coeffiecients​

Step 4: Draw synthetic division bar

Step 5: Input coefficients​

​Step by Step (cont.)

Step 6: Use k opposite number of divisor.

Step 7: ​Bring first coefficient straight down.

​Step 8: Multiply k by new number.

​Step 9: Combine new numbers (add or subtract)

Step 10: ​Repeat steps 8 and 9.

​Step 11: Write quotient with new coefficients. One degree less that dividend.