Synthetic Division

Polynomial Division

Given a factor, how do we get other factors?

General Rules

For the example $s^3+8s^2+102s+180$ where we know $s+2$ is a factor…

• Write the coefficients of the standard form polynomial in a division table [1, 8, 102, 180]
• Since $s+2$ is a factor, the divisor is $-2$
• Always bring down the first coefficient to the result row ($1$ in this case)
• Multiply the divisor by the first coefficient $-2\cdot 1=-2$ then add to the next coefficient $-2+8=6$ which you write under the next coefficient
• Repeat this process until one of your results is a 0
• In this case we end up with [1, 6, 90, 0] which corresponds to $s^2+6s+90$