Homework LogMon

12/14

Lesson 5 – 1

Learning Objective: To divide polynomials using long division & synthetic division

Hw: #501 Pg. 277 1 – 33 odd, skip 23

12/14/15 Lesson 5 – 1 Synthetic Division Day 1

Advanced Math/Trig

Learning Objective To divide polynomials using long division

To divide polynomials using synthetic division

Dividing Polynomials

OR

Long Division: Rewrite in descending order & fill in any missing terms with 0

Dividend = (Divisor)(Quotient) + Remainder

𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝐷𝑖𝑣𝑖𝑠𝑜𝑟 =𝑄𝑢𝑜𝑡𝑖𝑒𝑛𝑡+ 𝑅𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟

𝐷𝑖𝑣𝑖𝑠𝑜𝑟

1. Divide by Long Division

4 𝑥2−3 𝑥+2 8 𝑥3−18𝑥2+11𝑥−62

8 𝑥3−6 𝑥2

– 6

– 3

+ 4−12 𝑥2 + 7x

–– 6

+ 9x

–– –

– 2x–12

R

–

–

Quotient

Remainder

Descending Order!

(2 𝑥−3 ) (4 𝑥2−3 𝑥+2 ) −2𝑥

2.

Divide using Synthetic Division

=

x = 44𝑥3 𝑥2 𝑥¿2 −13 26 −24

28−5

−206240

𝑥2 𝑥¿ 𝑅

3.

Divide using Synthetic Division

=

x = –2– 2𝑥3 𝑥2 𝑥¿02 −4 12

−81618

−36−408092

𝑥2 𝑥¿ 𝑅

𝑥44

4𝑥3

−8

4. Divide by long division

3x + 1 +0𝑥3

3 𝑥4 +

– 2

– 6 + – 6

–

– 23

–

– –+ 7

+

3 + – – 6 + 0

+ 2

6x + 2– – – 2

–

5.

Divide using Synthetic Division

Need to divide by 3

x = 𝑥3 𝑥2 𝑥¿−5 17 0

−623

−16

−2−2

𝑥2 𝑥¿ 𝑅

𝑥43

3𝑥3

−1

=

6.

Divide & write answer as Dividend = (Divisor)(Quotient) +

Remainder

x = –3

– 3𝑥2 𝑥¿20 −5

−133

−9−14𝑥¿ 𝑅

𝑥31

1𝑥2

−3

Divisor QuotientRemainder

7. is divided by

Find quotient Q(x) & the remainder r when

r = 0

x = –2– 2𝑥2 𝑥¿00 8

−244

−80𝑥¿ 𝑅

𝑥31

1𝑥2

−2

Ticket Out the Door Divide by Long Division Divide by Synthetic Division Do you get the same answer?

Homework#501 Pg. 277 1 – 33 odd, skip

23

2. Divide

5x + 5 10 𝑥6+5 𝑥5+0𝑥4+10𝑥3+0𝑥2−20 𝑥−152

10 𝑥6+10

–

– 5 +0 – 5

–

– 55

–– –

+0 +0

+10

+

5 +5– – 5 + 0

+

5 + 5– – -5 – 20x

–

– 5 – 5– – – 15x – 15

– 3