1.

Warm – up #2

r =

Find the remainder when P(x) is divided by x – c

−𝑖𝑥3 𝑥2 𝑥

−2 𝑖 𝑖 0

00𝑖11

𝑥2 𝑥 ¿

𝑥4−2

−2𝑥32 𝑖

¿2−𝑖2−𝑖𝑅

Homework LogWed

12/16

Lesson 5 – 2

Learning Objective: To use the Remainder Theorem to find P(c)

Hw: #503 Pg. 285 #1 – 23 odd

12/16/15 Lesson 5 – 2 Remainder Theorem Day 1

Advanced Math/Trig

Learning Objective To use the Remainder Theorem to find P(c)

Remainder Theorem

If a polynomial P(x) is divided by x – c, the remainder is P(c).

Use Remainder Theorem & Synthetic Division to find P(c)

1. c = 2

2𝑥3 𝑥2 𝑥¿01 4 −9

10202142469283𝑅

𝑥45

510 Remainder

P(2) = 83

= 83

Use Remainder Theorem & Synthetic Division to find P(c)

2. c =

2−𝑖𝑥3 𝑥2 𝑥 ¿0 −3 4 0

2−𝑖3−4 𝑖

−4 𝑖−4−8 𝑖−8 𝑖

−8−16 𝑖−8−16 𝑖𝑅

𝑥41

12−𝑖

Remainder𝑃 (2− 𝑖 )=−8−16 𝑖

3. Find Remainder by Long Division

x – 1 2 𝑥4−3 𝑥3+0 𝑥2+4 𝑥−52 𝑥3

2 𝑥4−2 𝑥3–

– + –

–

+ −𝑥2

–

– –+ 4

−𝑥

−𝑥2+ – – 3 – 5

+ 3

3x – 3– –

– 2

–

Use Remainder Theorem to find the remainder of

4. c = 1

1𝑥3 𝑥2 𝑥¿−3 0 4 −5

−1−1−1

−133−2

𝑥42

22 Remainder

P(1) = –2 = –2

Use Remainder Theorem to find the remainder of

5. c = 1 = 1 – 17 + 9= – 7

Use Remainder Theorem to find the remainder of

6.

2 𝑖𝑥2 𝑥 ¿1 1 1

1+2 𝑖−4+2 𝑖−3+2 𝑖

−4−6 𝑖−3−6 𝑖𝑅

𝑥31

12 𝑖

𝑃 (2𝑖 )=−3−6 𝑖

= =

Ticket Out the Door Use the Remainder Theorem to find the remainder

Homework#503 Pg. 285 #1 – 23 odd