chapter 3 quiz 1 review – answers to practice problems 6...

Math 2B/3A

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10

Chapter3Quiz1Review–AnswerstoPracticeProblems1.

a. 9𝑥! + 30𝑥 + 19b. 3𝑥! − 13

2. a. 𝑝 𝑥 = −6𝑥! − 2𝑥! + 2𝑥 + 4b. −6c. 3d. 𝑟 𝑥 = −3𝑥! + 3𝑥! − 1e. 𝑞 𝑥 = 6𝑥! + 2𝑥!f. −2g. 𝑞(𝑥)isabinomialand𝑟(𝑥)isatrinomial

3. a. Answersvary,𝑔(𝑥)musthavedegree3.b. Answersvary,𝑘(𝑥)musthavedegree3.c. 𝑚 𝑥 = 3𝑥! − 4𝑥 − 6d. −4𝑥e. −6

4. Answersvary,possibleanswersaregiven

a. 𝑥 − 4b. 𝑥! + 3𝑥 + 1c. 4𝑥!d. 𝑥! + 2𝑥!

5. a. 3𝑥 − 4 2𝑥 − 7 b. 2𝑥 + 1 𝑥 − 1 c. 4𝑥!(3𝑥 − 1)d. 5𝑥𝑦 𝑥 + 3𝑦 − 4

6. a. 𝑥 − 7 𝑥 + 1 b. 𝑥 + 7 𝑥 − 5 c. (𝑥 + 6)(𝑥 + 12)d. 𝑥 − 8 𝑥 − 3 e. Theyareallmonictrinomialswithrelatively

smallconstantterms.7.

a. 7𝑦 + 8 7𝑦 − 8 b. 𝑚 + 4 + 5 𝑚 + 4 − 5 =

𝑚 + 9 𝑚 − 1 c. (11 + 4𝑝)(11 − 4𝑝)d. (9𝑘! + 10𝑚)(9𝑘! − 10𝑚)e. Theyarebinomialswherebothtermsare

prefectsquaresandthesecondtermisbeingsubtracted.

8. a. 2𝑥 + 1 3𝑥 − 5

b. (𝑥 − 6)(5𝑥 − 3)c. (4𝑥 + 3)(𝑥 − 1)d. (2𝑥 − 3)(3𝑥 + 4)e. Theyarenon-monictrinomials

9. a. (𝑥 − 14)(𝑥 + 8)b. 𝑥 + 10 𝑥 + 11 c. (𝑥 − 11)(𝑥 − 9)d. sorry,thisoneisn’tnice,skipit!e. Theyaremonictrinomialswitharelatively

largeconstantterm.10.

a. SumsandProducts 𝑥 + 3 𝑥 + 9 b. CompletingtheSquare 𝑥 − 15 𝑥 + 7 c. GCFFactoring𝑥!(2𝑥 − 5)d. SumsandProducts(5𝑥 − 1)(𝑥 + 3)e. Diff.ofSquares(5𝑥! + 12)(5𝑥! − 12)f. SumsandProducts 𝑥 − 9 (𝑥 − 3)g. DifferenceofSquares(2𝑥 + 3)(2𝑥 − 3)h. CompletingtheSquare(𝑥 − 16)(𝑥 − 12)i. SplittingtheMiddleTerm(3𝑥 − 4)(𝑥 + 7)j. GCFFactoring4𝑥𝑦!(4𝑥! − 𝑥𝑦 + 2)

11. a. 5𝑥(𝑥 + 4)(𝑥 − 1)b. 𝑥(3𝑥 + 2)(4𝑥 − 5)c. 4𝑥! + 1 2𝑥 + 1 2𝑥 − 1 d. 2 𝑥 − 7 𝑥 − 7 or2(𝑥 − 7)!e. 3𝑥 5𝑥 + 3 5𝑥 − 3 f. 𝑥 𝑥 + 12 𝑥 − 2 g. 3𝑥 𝑥 − 5 𝑥 + 3 h. 4(2𝑥 + 1)(𝑥 − 3)

12. a. 𝑥 = −2,−7b. 𝑥 = −8,−5c. 𝑥 = −15, 11d. 𝑥 = ± !

!

e. 𝑥 = −2 ± 3f. 𝑥 = −2 ± !

!

13. a. oneRealsolutionb. noRealsolutionsc. 2Realsolutionsd. 2Realsolutions