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Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...•...

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Problem A = 2 ! − 7 ! + 29 ! + 141 ! − 773 + 348 Guidelines • Each person in the group needs to actively participate in the poster’s creation. • Each person needs to pick a different color to write with. • Each person needs to write his/her name on the front of the poster in the chosen color. • All colors need to be equally represented in the solution to the given problem. Your poster should contain: • The original polynomial function • The equivalent factored form of the original polynomial • Work showing how each factor was found. You can use the graph or the table to determine TWO of the zeroes. Approved methods for factoring include long division and/or quadratic formula. • Graph of the function. Problem B = 6 ! + 17 ! − 76 ! − 292 − 240 Guidelines • Each person in the group needs to actively participate in the poster’s creation. • Each person needs to pick a different color to write with. • Each person needs to write his/her name on the front of the poster in the chosen color. • All colors need to be equally represented in the solution to the given problem. Your poster should contain: • The original polynomial function • The equivalent factored form of the original polynomial • Work showing how each factor was found. You can use the graph or the table to determine TWO of the zeroes. Approved methods for factoring include long division and/or quadratic formula. • Graph of the function.
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Page 1: Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...• The original polynomial function • The equivalent factored form of the original

ProblemA

𝑓 𝑥 = 2𝑥! − 7𝑥! + 29𝑥! + 141𝑥! − 773𝑥 + 348Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineTWOofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

ProblemB

𝑓 𝑥 = 6𝑥! + 17𝑥! − 76𝑥! − 292𝑥 − 240Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineTWOofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

Page 2: Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...• The original polynomial function • The equivalent factored form of the original

ProblemC

𝑓 𝑥 = 𝑥! − 5𝑥! + 9𝑥 − 45Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineONEofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

ProblemD

𝑓 𝑥 = 8𝑥! + 34𝑥! + 32𝑥 + 6Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineONEofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

Page 3: Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...• The original polynomial function • The equivalent factored form of the original

ProblemE

𝑓 𝑥 = 3𝑥! − 17𝑥! − 7𝑥! + 73𝑥 + 60Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineTWOofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

ProblemF

𝑓 𝑥 = 𝑥! + 13𝑥! + 4𝑥 + 52Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineONEofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

Page 4: Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...• The original polynomial function • The equivalent factored form of the original

ProblemG

𝑓 𝑥 = 16𝑥! + 12𝑥! − 94𝑥! + 48𝑥! + 18𝑥Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineTWOofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

ProblemH

𝑓 𝑥 = 2𝑥! + 3𝑥! − 4𝑥! − 3𝑥 + 2Guidelines

• Eachpersoninthegroupneedstoactivelyparticipateintheposter’screation.• Eachpersonneedstopickadifferentcolortowritewith.• Eachpersonneedstowritehis/hernameonthefrontoftheposterinthechosencolor.• Allcolorsneedtobeequallyrepresentedinthesolutiontothegivenproblem.

Yourpostershouldcontain:

• Theoriginalpolynomialfunction• Theequivalentfactoredformoftheoriginalpolynomial• Workshowinghoweachfactorwasfound.YoucanusethegraphorthetabletodetermineTWOofthezeroes.

Approvedmethodsforfactoringincludelongdivisionand/orquadraticformula.• Graphofthefunction.

Page 5: Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...• The original polynomial function • The equivalent factored form of the original

Name________________________________________________________Period_____________Date_______________

FactoringPosterRecordingSheetVisiteachpostertocompletethetablebelow

ProblemA𝑓 𝑥 = 2𝑥! − 7𝑥! + 29𝑥! + 141𝑥! − 773𝑥 + 348

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

ProblemB𝑓 𝑥 = 6𝑥! + 17𝑥! − 76𝑥! − 292𝑥 − 240

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

ProblemC𝑓 𝑥 = 𝑥! − 5𝑥! + 9𝑥 − 45

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

ProblemD𝑓 𝑥 = 8𝑥! + 34𝑥! + 32𝑥 + 6

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

ProblemE𝑓 𝑥 = 3𝑥! − 17𝑥! − 7𝑥! + 73𝑥 + 60

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

Page 6: Polynomial Factoring Poster Problems - Weeblymrtrenfield.weebly.com/uploads/5/8/6/1/58616339/...• The original polynomial function • The equivalent factored form of the original

ProblemF𝑓 𝑥 = 𝑥! + 13𝑥! + 4𝑥 + 52

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

ProblemG𝑓 𝑥 = 16𝑥! + 12𝑥! − 94𝑥! + 48𝑥! + 18𝑥

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

ProblemH𝑓 𝑥 = 2𝑥! + 3𝑥! − 4𝑥! − 3𝑥 + 2

FactoredForm

Degree #ofrealzeroes #ofcomplexzeroes #offactors

Summary1)Makeaconjectureabouttherelationshipbetweenthedegreeofapolynomialandthenumberoffactorsapolynomialhas.2)Makeaconjectureaboutthedegreeofthepolynomial,thenumberofrealroots,andthenumberofcomplexroots.3)Makeaconjectureaboutthenumberofcomplexrootsapolynomialhas.Application1)Youareaskedtofactor𝑓 𝑥 = 15𝑥! + 32𝑥! + 841𝑥! + 12𝑥 − 50.Howmanyfactorsdoesthispolynomialhave?2)Whenfactoring𝑓 𝑥 = 𝑥! − 6𝑥! + 9𝑥 − 54,Mr.Trenfield’sanswerkeystated6and3𝑖aretheonlyroots.Whataretworeasons(withoutsolving,baseduponyourconjectures)youknowthereisanerrorinthekey.


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