1. Divide using long division
Homework Quiz 3.2
Divide using long division
( 𝑥 3 + 3𝑥 2 −𝑥+2)÷(𝑥−1)

2. 3.3 Synthetic Division and Remainder Theorem
EQ: How do you use synthetic division and the remainder theorem

3. Refresher
( 3𝑥 3 +5𝑥+7)÷(𝑥+4)

4. Synthetic Division
Used to simplify long division, when dividing by a linear expression 𝑥−𝑎
Use synthetic division to divide 𝑥 3 −57𝑥+56 by 𝑥−7.
What is the quotient and remainder
When we have 𝒙−𝟕 we will take −𝟕 and reverse the sign to +𝟕.
Then write the coefficients of the polynomial. All the coefficients, including zeros. +7 −
Step 1: set up synthetic division

5. +7 1 0 −57 56 1 +7 1 0 −57 56 1 Step 2 bring down first coefficient− 1
Step 3 multiply the coefficient by the divisor. Then add to the next coefficient +7 − 1

6. Example 1 Divide using Synthetic Division
( 3𝑥 3 +5𝑥+7)÷(𝑥+4)

7. Example 2 Divide using Synthetic Division
( 2𝑥 3 −5𝑥+7)÷(𝑥−2)

8. The Remainder Theorem P(x) 𝑥−𝑎
If you divide a polynomial P(x) of degree n≥1 by 𝑥−𝑎, then the remainder is P(a)
Example 3
P(x)
𝑥−𝑎
( 2𝑥 3 −5𝑥+7)÷(𝑥−2)
( 3𝑥 3 +5𝑥+7)÷(𝑥+4)

9. Example 4
Given the P(x) = 𝑥 5 − 3𝑥 4 − 28𝑥 3 +5𝑥+20, what is P(-4)

10. Exit Ticket
If the polynomial P(x) is divided by x-a and the remainder is 0, what conclusion can we make?

11. Homework p
#23-27 odd, odd, 41, 42