Warm – up #2 Find the remainder when P(x) is divided by x – c.
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Transcript of Warm – up #2 Find the remainder when P(x) is divided by x – c.
![Page 1: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/1.jpg)
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
![Page 2: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/2.jpg)
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
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12/16/15 Lesson 5 – 2 Remainder Theorem Day 1
Advanced Math/Trig
![Page 4: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/4.jpg)
Learning Objective To use the Remainder Theorem to find P(c)
![Page 5: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/5.jpg)
Remainder Theorem
If a polynomial P(x) is divided by x – c, the remainder is P(c).
![Page 6: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/6.jpg)
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
![Page 7: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/7.jpg)
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
![Page 8: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/8.jpg)
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
–
![Page 9: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/9.jpg)
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
![Page 10: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/10.jpg)
Use Remainder Theorem to find the remainder of
5. c = 1 = 1 – 17 + 9= – 7
![Page 11: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/11.jpg)
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
= =
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Ticket Out the Door Use the Remainder Theorem to find the remainder
![Page 13: Warm – up #2 Find the remainder when P(x) is divided by x – c.](https://reader036.fdocuments.net/reader036/viewer/2022081507/5a4d1b3a7f8b9ab05999e24e/html5/thumbnails/13.jpg)
Homework#503 Pg. 285 #1 – 23 odd