1. Section 2-2 Synthetic Division; The Remainder and Factor Theorems

2. Recall… Polynomial long division is like long division with numbers.

3. The Remainder Theorem When a polynomial P(x) is divided by x – a, the remainder is P(a).

4. Synthetic Division Since synthetic substitution gives not only the remainder but also the quotient, we can use it in place of long division, this is called synthetic division.

5. The Factor Theorem For a polynomial P(x), x – a is a factor if and only if P(a) = 0.

6. Example Find the quotient and remainder when is divided by x + 4

7. Example If x = 2 is a root of find the remaining roots.

8. Example When a number is divided by 5 the quotient is 7 and the remainder is 2. Find the number.

9. Example When a polynomial P(x) is divided by 3x – 4, the quotient is and the remainder is -1. Find P(x).