[PDF] x^r Practice and Problem-Solving Exercises - Miami Arts Charter PDF Alg%201%20Ch%208%20Problems.pdf

23 jan 2015 · Error Analysis Describeand correct the error in finding the difference of the polynomials (4x^ frame? Write your answer in factored form 28

Factoring Packet Directions: Practice Practice Practice Practice Practice Practice Practice Practice Practice 7-2 Practice Worksheet Factoring Using the Distributive Property Complete 1 Reteaching Worksheet Summary of Factoring

[PDF] FACTORING POLYNOMIALS

BE SURE YOUR ANSWERS WILL NOT FACTOR FURTHER All answers may be checked by multiplication Page 2 PRACTICE PROBLEMS:

[PDF] Factoring Practice

Factoring Practice I Greatest Common Factor (GCF) Find the GCF of the numbers 1 12, 18 2 10, 35 3 8, 30 4 16, 24 5 28, 49 6 27, 63 7 30, 45 8 48, 72

[PDF] Factoring Polynomials:

Classwork/Practice Packet Lesson 1: Factoring Binomials that are the Difference of Two Perfect Squares pg 9 Factoring with Pizzazz worksheets pg 16-30

[PDF] factoring-worksheet-hw-4-27

Algebra Worksheet - Section 10 5 Factoring Polynomials of the form x2 + bx + c Name Block Black Factor 1 x2 + 3x + 2 2 x2 – x-2 3 x2 +x-6 4 a? +a-12

[PDF] Algebra - White Plains Public Schools

Practice: Factor each polynomial using the GCF and check your answer 1 6 Challenge Problem: Factor 12a 2 bc 2 - 24a 4 c Summary: Exit Ticket: 1) 2)

[PDF] Dec 9 ANSWER KEYpdf

le Chapter Summary and view begins with an greatest common factor, GCF 257 256 prime number perfect square -10 Practice Worksheet re Solving

[PDF] Factoring, Solving Equations, and Problem Solving - CDN

Factoring polynomials will allow us to solve Solve Word Problems Using Factoring Because 0 is not a reasonable answer to the problem, the solution is 8 The solution 8 is not possible for the width of a rectangle, so the plot is 2 meters

[PDF] Factoring Packetpdf

21 NAME Student Edition Practice Pages 565–571 Factoring Using the Distributive Property Complete 1 8m - 6 = 2(4m - 3) 2 36a2 + 2462 = 12_3a² + 262)

[PDF] x^r Practice and Problem-Solving Exercises - Miami Arts Charter

23 jan 2015 · Error Analysis Describeand correct the error in finding the difference of the polynomials (4x^ frame? Write your answer in factored form 28

HowcanProblem4

help yousolvethis problem?

Changethe subtraction

toadditionbyadding theopposite.

Thenuse

theverticalorhorizontal methodfromProblem4 to addthepolynomials.

Recallthatsubtractionmeanstoadd

changeeachof thetermsto itsopposite.Thenaddthecoefficients.

2»7Problem5SubtractingPolynomials

Whatisasimplerformof(x3 - 3x2 + 5x) - (7x3 + 5x2-12)?

Method1Subtractvertically.

x3 - 3x2 + 5xLineup liketerms. - (7s3 +5x2- 12)

3 _o2_i_cyThenaddtheoppositeofeachtermin

thepolynomialbeingsubtracted. -7x3-5x<+12 -6x3- 8x2+5x +12

Method2Subtracthorizontally.

(x3-

3x2+5x)-{7x3+5x2-12)

the polynomialbeing subtracted. =(x3-7x3)+ (-3x2 -5x2)+5x+12Groupliketerms. =-6x3-8x2+ 5x + 12Simplify. t£ ^5^

LessonCheck

DoyouknowHOW?

Findthedegreeofeachmonomial.

1. -7x42.8y2z3

Simplifyeachsumordifference.

3.(5r3+ 8) +(6r3+ 3)

4. (x2-2) -(3x+ 5)

DoyouUNDERSTAND?

VocabularyNameeachpolynomialbasedon itsdegree

andnumberofterms.

5.5x2 + 2x + 16.3z - 2

7.CompareandContrastHow aretheprocessesof

How are

theprocessesdifferent? x^rPractice andProblem-SolvingExercises

WffPractice

Findthedegreeofeachmonomial.

8. 3x9. 8a3

12.-ifz13.-3

4pSee Problem 1.

10.20

14.12u/415.0

©Apply

Simplify.

16.12p2

20.x3 -9xr

Qp'17.2mBn3+9m3n318.8w2x+w2x

21.30v4w3-\2v4w322.7x2- 2x2

onitsdegreeandnumberofterms. ^PSee Problem2.

19.3t4+lit4

23.5bc4 -I3bc4

4pSee Problem3.

24.5y -

2y2

27.6x2 -13.V2-Ax +4

Simplify.

30.4w- 5

+9w+ 2

33.(5x2+ 3) +(l5x2+2)

25.-2^+ 7

28.c + 8c3 - 3c7

31.6.v-+ 7

+3jc2+ 1

26.x2+ 4 -3*

29.3z4-5z-2z2

^See Problem 4.

32.2fc2-ik+ 3

+5Jfc2+3k - 7

34.(2g4-3g+9)+(-g3+12g)

35. EducationThenumberofstudentsat EastHighSchool and thenumberof

studentsatCentralHigh School over a 10-yearperiodcan bemodeledbythe followingpolynomials.

EastHighSchool: - Hjc2+133x+1200

CentralHighSchool:-7x~+95.v + 1100

Ineachpolynomial,x= 0correspondsto the first year in the10-yearperiod.What polynomialmodels

Simplify.

36.5/z- 2

-(3/2+ 8)

39.(14/24+3ft3)-(9/24+2/23)

37.6.v3 + 17

-(4x3+9)

4(JSee Problem 5.

38.2c2 +7c -1

- (c2 - 10c + 4)

40.(-6m;4+u/2)-(-2m;3+4w2-w)

41. ThinkAbout aPlanTheperimeterofatriangularparkis16.v+ 3.

Whatisthemissinglength?

•Whatisthesumofthetwo given sidelengths? •Whatoperationshouldyou use to find theremainingsidelength?

42.GeometryTheperimeterofa trapezoid is39a- 7.Three sides

have the followinglengths:9a,5a +1,and17a - 6. What isthe lengthofthefourthside?

43.ErrorAnalysisDescribeand correcttheerrorinfindingthedifferenceof

thepolynomials. (4x^dj^5x- 6)=4x2^_xji-3-~3x2-=-15x":r6 cLx-5x+3-6 = x2 -6x- 3 5x-1

478Chapter8PolynomialsandFactoring

Simplify.Writeeachanswerinstandardform.

44.(5x2-3x+7x)+(9x2+2x2+7x)

46.(-9r3 +2r-l)- (-5r2+ r +8)

45.(y3-4y2- 2) -(6y3+ 4 -6y2)

47.(3z3- 4z +7z2)+(8z2- 6z- 5)

48.ReasoningIs itpossibletowriteatrinomialwithdegree0?Explain.

49.WritingIsthesumof twotrinomialsalways atrinomial?Explain.

iMChallenge50.a. Write theequationsforlinepand lineq.Useslope-interceptform. b. Use yourequationsfrompart(a) to write afunctionfor the thesamex-value. c. ForwhatvalueofxdoesD(x)equalzero? d.

Simplifyeachexpression.

51.(ab2+ba3)+(4a3b-ab2-5ab)

52.(9pq6-Up4q)-{~5pq6+p4q4)

SunshineStateStandardsPractice

y pf q b -2 0) \6 X

MA.912.A.3.12

MA.912.A.4.2

-x2+ X-10CDx2-x +10CO7x2 +llx+

54.Thepriceof a giftbasketof foodcanbemodeledby alinearequation.Youcan

use thegraphattheright to find the price of thebaskety,basedonpoundsof foodx.Whatistheequationoftheline?

CDy=5x+io<3Dy = 10*+ 5

CDy = x +10CDy =10x+ 10

55.ShortResponseSimplify(8x3-5x+1)-(x2+ 4).Showyourwork.

7xl+11*+10

20 10 0 x r

MixedReview

56. y = 7 • 3* 57.y =0.3 •2.1*58. y = 3 •4X

60. (0, 2), (5, 0) 61.(3,

-7),(4, 1) 62.(-2,8), (1, 0)

GetReady!Toprepare forLesson8-2,doExercises64-67.

Simplifyeachexpression.

64.a~3a865.6r2•3r66.(4x5)(7x3)

4&SeeLesson 7-7.

59. y = 0.2 •5*

4DSee Lesson5-1.

63.(9,-6),(0, 0)

4pSee Lesson7-3.

67.{2t4)(-5t2)

f Plan

How can you findthe

shadedregion'sarea?

Theshaded region isthe

entire square except for thecircularportion.So, subtracttheareaofthe circle fromtheareaof the square. •-NA

3&WProblem4FactoringaPolynomialModel

factoredform.

Step1Findtheareaoftheshadedregion.

Ai=s2Areaofasquare

=(2x)2Substitute2xfors. =4x2Simplify.

A2=KJ2Area of a circle

Substitutex for r.=KX2

Theareaoftheshadedregionis

A} - An,or4.v2

-2 JTX

Step2Factortheexpression.

FirstfindtheGCF.

Ax2= 2 • 2 • a •a

nx2=n• x • x

TheGCFisx• a,orx.

Step3FactorouttheGCF.

4x2 -nx2 =a:'(4)+a-(-;t)

-a'(4-n) GotIt?4. In Problem4,supposethe sidelengthofthesquare is6xand the radiusofthe 4

LessonCheck

DoyouknowHOW?

1.Whatisasimplerformof6x(2x3+7x)?

2.WhatistheGCFofthetermsin4a4 +6a2?

Factoreachpolynomial.

3.6m2 - 15m

DoyouUNDERSTAND?

Matcheachpairofmonomialswithits GCF.

5.14/z2,35/z4A.1

6.21/23,18n2B.7n2

7/r,9C.3n2

itsterms.

4.4x3+8x<12*

482Chapter8 Polynomials and Factoring

^ap?PracticeandProblem-SolvingExercises

WffPractice

©Apply

Simplifyeachproduct.

9.7.x(.x+ 4)

12.-w\w-15)

10.{b +11)2/;

13.4x(2.x37x2

FindtheGCFofthetermsofeachpolynomial.

15.12x+20

18.a3 + 6a2 -lla

Factoreachpolynomial.

21.9.x- 6

24.5k3 + 20k2 -15

16.8a/2-Ww

19.4x3+ 12x - 28

22.t2 +8t

25.14x3 - 2x2 +8x

4f*SeeProblem 1.

11.3/?22(10+m)

14.-8y\7y2-Ay-1)

^gSeeProblem 2.

17.A5b+27

20.14z4-42z3+21z2

4^See Problem 3.

23.14/r3-35/?2+ 28

26.fi4+24g3+12g2+Ag

27.ArtAcircularmirror issurroundedbyasquare metal frame.Theradius ofthe4(JSee Problem 4.

mirroris 5x. Thesidelengthofthemetalframeis 15x.Whatis theareaofthemetal frame?Write youranswerinfactoredform.

28.DesignAcirculartableispaintedyellow with a redsquareinthemiddle.The

radiusofthetabletopis 6x. Thesidelengthof the redsquareis 3x.Whatisthe area of the yellowpartof thetabletop?Write youranswerin factored form.

Simplify.Writeinstandardform.

29. -2x(5x2 - 4x +13)30.-5y2(-3y3+8y)

32.p{p+2)-3p(p-5) 33.t2{t+1)-t{2t2-1)

31.10a(-6rt2+2fl- 7)

34.3c(4c2- 5) -c(9c)

35. ThinkAbouta PlanArectangularwoodenframe has sidelengths5.xand7.x+ 1.

Therectangularopeningfor apicturehas sidelengths3x and5x.What is the area of

Howcandrawingadiagramhelpyou solve theproblem?

•Howcanyouexpresstheareaof thewoodenpartoftheframeas adifference ofareas? inmultiplying.

Factoreachpolynomial.

40.a.Factorrr+n.

b.WritingSupposenisaninteger.Is/?2+nalways,sometimes,orneveran even integer?Justifyyouranswer. i

Justifyyouranswer.

out ofit.TheformulaforthevolumeofacylinderisV=Ki2h,whereris theradiusandhistheheight. b. Write aformulafor thevolumeof thecylinderintermsofs. cylinderhasbeenremoved. d.Factoryourformulafrompart(c). e.FindVincubicinchesfors =15in.Usek=3.14.

43.a.GeometryHowmanysidesdoesthepolygonhave?Howmanyof its

diagonalscomefromonevertex? b. Apolygon has/?sides. Howmany diagonals willit have from one vertex? polynomialinstandardform. d.Apolygonhas 8 sides. Howmanydiagonalsdoes ithave? *2 r *i q-(

SunshineStateStandardsPractice

MA.912.A.4.244.Simplifythe product4.x(5.x2+ 3x + 7).Whatisthecoefficientofthex2-term? MA.912.A.3.146.Whatisthesolutionoftheequation7.x- 11 = 3? MA.912.A.4.348. Theexpression9X3-15.xcanbefactoredasax^x2-5).

[PDF] [PDF] x^r Practice and Problem-Solving Exercises - Miami Arts Charter

HowcanProblem4

Changethe subtraction

Thenuse

Recallthatsubtractionmeanstoadd

2»7Problem5SubtractingPolynomials

Method1Subtractvertically.

3 _o2_i_cyThenaddtheoppositeofeachtermin

Method2Subtracthorizontally.

3x2+5x)-{7x3+5x2-12)

LessonCheck

DoyouknowHOW?

Findthedegreeofeachmonomial.

1. -7x42.8y2z3

Simplifyeachsumordifference.

3.(5r3+ 8) +(6r3+ 3)

DoyouUNDERSTAND?

VocabularyNameeachpolynomialbasedon itsdegree

5.5x2 + 2x + 16.3z - 2

7.CompareandContrastHow aretheprocessesof

How are

WffPractice

Findthedegreeofeachmonomial.

8. 3x9. 8a3

12.-ifz13.-3

4pSee Problem 1.

14.12u/415.0

©Apply

Simplify.

16.12p2

20.x3 -9xr

Qp'17.2mBn3+9m3n318.8w2x+w2x

21.30v4w3-\2v4w322.7x2- 2x2

19.3t4+lit4

23.5bc4 -I3bc4

4pSee Problem3.

24.5y -

27.6x2 -13.V2-Ax +4

Simplify.

30.4w- 5

33.(5x2+ 3) +(l5x2+2)

25.-2^+ 7

28.c + 8c3 - 3c7

31.6.v-+ 7

26.x2+ 4 -3*

29.3z4-5z-2z2

32.2fc2-ik+ 3

34.(2g4-3g+9)+(-g3+12g)

35. EducationThenumberofstudentsat EastHighSchool and thenumberof

EastHighSchool: - Hjc2+133x+1200

CentralHighSchool:-7x~+95.v + 1100

Simplify.

36.5/z- 2

39.(14/24+3ft3)-(9/24+2/23)

37.6.v3 + 17

4(JSee Problem 5.

38.2c2 +7c -1

40.(-6m;4+u/2)-(-2m;3+4w2-w)

41. ThinkAbout aPlanTheperimeterofatriangularparkis16.v+ 3.

Whatisthemissinglength?

42.GeometryTheperimeterofa trapezoid is39a- 7.Three sides

43.ErrorAnalysisDescribeand correcttheerrorinfindingthedifferenceof

478Chapter8PolynomialsandFactoring

Simplify.Writeeachanswerinstandardform.

44.(5x2-3x+7x)+(9x2+2x2+7x)

46.(-9r3 +2r-l)- (-5r2+ r +8)

45.(y3-4y2- 2) -(6y3+ 4 -6y2)

47.(3z3- 4z +7z2)+(8z2- 6z- 5)

48.ReasoningIs itpossibletowriteatrinomialwithdegree0?Explain.

49.WritingIsthesumof twotrinomialsalways atrinomial?Explain.

Simplifyeachexpression.

51.(ab2+ba3)+(4a3b-ab2-5ab)

52.(9pq6-Up4q)-{~5pq6+p4q4)

SunshineStateStandardsPractice

MA.912.A.3.12

MA.912.A.4.2

54.Thepriceof a giftbasketof foodcanbemodeledby alinearequation.Youcan

CDy=5x+io<3Dy = 10*+ 5

CDy = x +10CDy =10x+ 10

55.ShortResponseSimplify(8x3-5x+1)-(x2+ 4).Showyourwork.