College Algebra & Trigonometry, 2018a

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2.7. SYNTHETIC DIVISION 125 2x 3 +4x 2 − 3x x − 5 ) 2x 4 − 6x 3 − 23x 2 +16x − 5 − 2x 4 +10x 3 4x 3 − 23x 2 − 4x 3 +20x 2 − 3x 2 +16x 3x 2 − 15x The last part of our answer will come from multiplying the −3 in the answer times the 5 in the divisor (making −15) and combining this with the +16 in the polynomial we’re dividing into: 2x 3 +4x 2 − 3x +1 x − 5 ) 2x 4 − 6x 3 − 23x 2 +16x − 5 − 2x 4 +10x 3 4x 3 − 23x 2 − 4x 3 +20x 2 − 3x 2 +16x 3x 2 − 15x 1x − 5 − x +5 0 The process of Synthetic Division uses these relationships as a shortcut to finding the answer. The set-up for a Synthetic Division problem is shown below: 5 2 −6 −23 16 −5
126 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS This set-up allows us to complete the division problem 2x4 − 6x 3 − 23x 2 +16x − 5 . x − 5 5 2 −6 −23 16 −5 The first coefficient in the answer is the same as the first coefficient in the polynomial we’re dividing into: 5 2 −6 −23 16 −5 ↓ 2 To get the next coefficient, we multiply the 2 by the 5 to get +10 and flll this in under the −6: 5 2 −6 −23 16 −5 ↓ +10 2 Then, −6+10=+4, which is the next coefficient in the answer: 5 2 −6 −23 16 −5 ↓ +10 2 4 Then, we continue this process, multiplying the 4 by the 5 to get 20 and combining this with the −23: −23+20=−3: 5 2 −6 −23 16 −5 ↓ +10 +20 2 4 −3 Next, multiply the −3 by the 5 and combine the resulting −15 with the 16: 5 2 −6 −23 16 −5 ↓ +10 +20 −15 2 4 −3 1
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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2
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
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14 CHAPTER 1. ALGEBRA REVIEW 1.2 Fa
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16 CHAPTER 1. ALGEBRA REVIEW Trinom
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18 CHAPTER 1. ALGEBRA REVIEW Here,
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20 CHAPTER 1. ALGEBRA REVIEW (3x ?)
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22 CHAPTER 1. ALGEBRA REVIEW which
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24 CHAPTER 1. ALGEBRA REVIEW Differ
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26 CHAPTER 1. ALGEBRA REVIEW If we
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28 CHAPTER 1. ALGEBRA REVIEW 25) 8y
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30 CHAPTER 1. ALGEBRA REVIEW Then,
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32 CHAPTER 1. ALGEBRA REVIEW We can
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34 CHAPTER 1. ALGEBRA REVIEW PROGRA
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36 CHAPTER 1. ALGEBRA REVIEW In mov
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38 CHAPTER 1. ALGEBRA REVIEW 1.4 Co
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40 CHAPTER 1. ALGEBRA REVIEW devise
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42 CHAPTER 1. ALGEBRA REVIEW −7i(
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44 CHAPTER 1. ALGEBRA REVIEW Exerci
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46 CHAPTER 1. ALGEBRA REVIEW 43) (3
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52 CHAPTER 1. ALGEBRA REVIEW The fa
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56 CHAPTER 1. ALGEBRA REVIEW the 4
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58 CHAPTER 1. ALGEBRA REVIEW The sa
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62 CHAPTER 1. ALGEBRA REVIEW 1.7 Ad
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64 CHAPTER 1. ALGEBRA REVIEW 7 x 2
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68 CHAPTER 1. ALGEBRA REVIEW 1.8 Co
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176 CHAPTER 3. EXPONENTS AND LOGARI
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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204 CHAPTER 4. FUNCTIONS Now, if, i
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206 CHAPTER 4. FUNCTIONS So the gra
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208 CHAPTER 4. FUNCTIONS Stretching
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210 CHAPTER 4. FUNCTIONS Multiplyin
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214 CHAPTER 4. FUNCTIONS 3) Match e
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216 CHAPTER 4. FUNCTIONS 6) f(x) 7)
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218 CHAPTER 4. FUNCTIONS Being fami
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222 CHAPTER 4. FUNCTIONS 4.6 Piecew
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226 CHAPTER 4. FUNCTIONS 4.7 Compos
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228 CHAPTER 4. FUNCTIONS 17) h(x) =
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230 CHAPTER 4. FUNCTIONS Original f
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232 CHAPTER 4. FUNCTIONS Then we sw
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234 CHAPTER 4. FUNCTIONS 19) f(x) =
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236 CHAPTER 4. FUNCTIONS 4.9 Optimi
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238 CHAPTER 4. FUNCTIONS 2) The gra
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242 CHAPTER 4. FUNCTIONS 8) A recta
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244 CHAPTER 4. FUNCTIONS So, our fi
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248 CHAPTER 4. FUNCTIONS Distance O
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250 CHAPTER 4. FUNCTIONS The graph
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252 CHAPTER 4. FUNCTIONS Distance/T
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254 CHAPTER 4. FUNCTIONS The graph
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256 CHAPTER 4. FUNCTIONS 3) A power
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258 CHAPTER 5. CONIC SECTIONS - CIR
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288 CHAPTER 6. SEQUENCES AND SERIES
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306 CHAPTER 7. COMBINATORICS differ
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308 CHAPTER 7. COMBINATORICS Exampl
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310 CHAPTER 7. COMBINATORICS 4) A c
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312 CHAPTER 7. COMBINATORICS 7.2 Fa
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314 CHAPTER 7. COMBINATORICS EXERCI
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316 CHAPTER 7. COMBINATORICS 7.3 Pe
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320 CHAPTER 7. COMBINATORICS 7.4 Ge
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322 CHAPTER 7. COMBINATORICS SET II
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324 CHAPTER 7. COMBINATORICS 22) A
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328 CHAPTER 7. COMBINATORICS Anothe
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330 CHAPTER 7. COMBINATORICS Exerci
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332 CHAPTER 7. COMBINATORICS The pr
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334 CHAPTER 7. COMBINATORICS Exampl
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336 CHAPTER 7. COMBINATORICS 4) Whe
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338 CHAPTER 7. COMBINATORICS 14) Fo
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342 CHAPTER 7. COMBINATORICS
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344 CHAPTER 8. RIGHT TRIANGLE TRIGO
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384 CHAPTER 9. GRAPHING THE TRIGONO
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438 CHAPTER 10. TRIGONOMETRIC IDENT
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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