**Key Terms**

- Descending Order – In order from highest power to lowest (exponents), from left to right.
- This is the standard way to write a polynomial.

- Dividend – The number to be divided.
- Divisor – The number being divided by.
- Quotient – The result of a division problem.
- Remainder – A number left over after dividing whole numbers. The letter r is sometimes used to represent a remainder.
- Synthetic Division – A process for dividing polynomials.
- This method is known as the “shortcut” for dividing polynomials because it requires fewer calculations than does long division.
- It ONLY works when the divisor is in linear form: .

**Review**

- Parts of Division Problems

- Integer Long Division with Fractional Remainder

- Polynomial Long Division (No Remainder)
- x≠-1 because -1+1=0, and you cannot divide by zero (undefined)

**Notes**

- Synthetic Division
- Always write polynomials in descending order (highest degree exponent first).
- Ex. should be rewritten in this order:

- If any terms are missing, insert them with a coefficient of zero.
- Ex. should be written , where the zero acts as a placeholder for the x-term.

- Synthetic Division is a shortcut for polynomial division
- Below are the STEPS for Solving with Synthetic Division

- Always write polynomials in descending order (highest degree exponent first).

- Take a look at step 2, above. The “a” of (x – a) is the divisor .
- Ex. If (x – 2) is your divisor, you would use “2” as your divisor term on the outside.
- Ex. If (x + 4), change it to (x – (-4)), and use “-4” as your divisor term on the outside.
- So, you should notice that you always use the opposite of whatever divisor you are given:
- Ex. (x – 6) would be +6
- Ex. (x + 3) would be -3

- Ex.
- First, rewrite the divisor as so that you know your “a” is -4.

- Remainders
- Synthetic division may have fractional remainders, just like integer division

**Examples**

- Ex 1: Synthetic Division Setup

- Ex 2. Solving with Synthetic Division