Algebra 2 Name

Assignment: Factoring· #1

PeriodI Date

A. Factor the greatest common factor (GCF) out of each expression.1. IOn3 -10n2 -8n 2. 4m8 + 2m5 + 12m43. 18n6 + 21n4 + 18n2

.2 Y\ (S-Vl ~--;- Y1 - 4)L t'Y\ 4 (2..h1 Lf + Vtl+ b)sn1..(tVJlf+ 1n2+t)

4. -32e - 40k2 - 24

5. -3Sp3 +70p-496. -9m4 -9m3 +4Sm2

_ ~ ( 4-k>--tsk'l-+~)-~(q-p>-IOp +1-)_ Qm'l--{h1L-+h1-S)

B. Factor each tetranomial by grouping. Remember to factor out the GCF first, if possible.-t. ISm3 + 10m2 +6m+4 8. 2r3 -7r2 + 8r - 28 9. 40k3 + 200k2 -lSk-7S

~ yn ').. (3\'Yl-p) -t 2-(3",+~ r-""( 'lr - 't) -t 4 (2r-'1-) 5 ( ~Ie' +4-0 Ie-'1.-_ 31v IS)(3r>1+ 2.) (S"""m'1--+ 2.-) I (2-r - T)( r '>-+ 4-) 5""[ & k l.U_: d - ')( Ie.t,~S- ( <is'Ie -.,) ( Ie- +S-)

Answer box for 1-9.

-8( 4e + Sk2 +3) (jp(2r2 - 4)(2r + 7)

3112(6114 + 7112 + 6)

-6(10e -Se +24)

(r2 + 4)(2r -7)

S(8e - 3)(k + S)

-9m2 (m2 + m - S) (j;)-7(Sp3 -10p+7) Q

211(S112-SI1-4)

2m4(2m4 +7n+6)

(Sm2 + 2)(3111+ 2)

-3m\Sm2 -m-S)

(40e -IS)(k + S)

7(Sp3 +10p+7)

7114(6116 +3112 +6)

4(r2 + 7)(2r - 4)

C. Write the letter of the factors in Column 2 for each trinomial in Column 1.

Column 1 Column 2

D3x2 -17x+24 A. (3x-4)(x-6)

G- 3x2 -34x-24

K (3x+8)(x-3)

r3x2 -18x +24 C. 3(x+1)(x+8)

E3x2 +21x-24 D. (3x-8)(x-3)

H3x2 -14x-24 E. 3(x+8)(x-1)

~

3x2 +3x-24 F. 3(x- 2)(x+4)

A3x2 -22x+24 G. (3x+2)(x-12)

F3x2 +6x-24 H.(3x+4)(x-6)

L3x2 +27x+24 I. 3(x- 4)(x - 2)

J. Prime

letelh trinomial

10. x2+6x 55

J.

11. 6x2 - 54x + 48,12. 2X2 -llx-21

lX +1\) (x-s)

, (X '2-_ q Y + g- )

( 2-X+3 )(X- i-)6 (x-K){X-Ij

13. 6n2 13n+ 7

14. x2 8115. x2 +lOx+25

(b K- f )(Y)-\)

lX+q)(X-~)L)(+~) 'l.."

D. Fact

'_I

16. 2a2 +2a 4 17. 3x2+39x+12018. 3n2-60n+300

2(61~+Ct+2-)

~ L X 1-+ I 3 )( + 4--0)'3 (n '2.-_ 2-D V1 +(00)

2 C Ct t 2-)(4 -l)

3( )(+ f ) (X+ S-))(n-ID)~

19. n2 +10n+15

20. 18n3 + 111n2 + 18n21. 60n3 -50n2 -40n"l..-

"'

Pyjrv-

~() ('VI'}..

\lD Vl (t VI - S-n -4.--J

-+19n+0 Ion (2Vl + I) C?> n - 4-___SVl ((n+\ )(n +0

,

Answer box for 10-21.

6(x - 5)(x - 8) prime (x + ll)(x - 5)

2n(lOn - 5)(3n + 4) (x + 5)2 I 3n(6n + 1)(n+

2(2a + 5)(a -1) (x + 5)(x - 5) 2(a + 2)(a -1)

(n-1)(6n-7)! JJ

3(n-10)2 (f1On(2n + 1)(3n - 4)

C3

i/

2(a - 2)(a +1) 6(x-1)(x- 8)

x+9)(x-9) (2x+3)(x-7) 1I

3(x + 5)( x + 8) prime

I Algebra 2

Assignment: Factoring -#2

NamePeriod Dat.e

A. Fact h tet . I b R, ber to factor out the GCF first. if b/,. ~~ ..1. 45x3 - 27 x2 + 60x - 36 2. 15x4 + 20x3 + 45x2 + 60x3.12x4-18x3+10x2-15x

Cj Xl-( ~)(-?,)+ 12.(~><-~5X~(~X+4) + I~X('3X+4)>( ( 1~')C'5_ /~)C 'l.-+ IO)t -I>)

r( ~~- ~)( '1)( .•..-\-12-)J

(3X+~)( ~X~+ (rx)X ( G Xfl)(-3) f 5(2)C-~~

1~)C (3X+tf)(x'l-+ 3))[X ( ~x-9(&/+9)

S(S;x-?) ('b X ~+<+~

.•.•.•......5>« '2.>>(3 +- Jf-X~ -/- q~ f-12)!J"'x( ~7-( 3X~) + 3(X~))5)( (3~-t-~(x:'2-+p

B. Write the letter of the factors in Column 2 for each trinomial in Column 1.

'tx+C)()(+V

C 'X-I !)(x-tV

ex +1Lf')Cx-~

.('1- (6){)t+-3)

('/.- 2lf)CX-~)

C X+4R) lx--U

( )C-~)Cx~)

C )(_12,) ()(-u)

('(+1 c,){ >a-0

c~-t\ 2..) lx-~

Column 1 Column 2..D

x2 +14x+48 ',51 PC (x+6)(x-8)

rx2 -8x-48-/2..,Lfa:' (x-2)(x-24)

F

x2 + 22x - 48 2...4-) - 2-.e:- (x+48)(x-l)

-:r

x2 -13x-48 -/61 3 6: (x+6)(x+8)

13

x2 - 26x+48 - 2-(./-; - 2-E:'" (x+ 16)(x-3)

Cx2 +47x-48Lf 91 -).,p: (x-2)(x+24)

A

x2 -2x-48 - <i/ ,G. (x-12Xx-4)

G- x2 -16x+48

_12/-\fW . (x-4)(x+12)

r=

x2 +13x-48 . tb,-3 Y(x+4)(x-12)

J-l

x2 +8x-48 12) -\fk (x+3)(x-16)..

6. x2 -14x+45 _ q)_~

(f-- ti)()( - r-)

7. 4n2 +52n+ 144 18. x2 -6x-16-9, 2-19. 3x2 -18x+15

(X-»)CX+:)I ~ ()( "l-_bY: + S-)

I ') ( x_S-)(.)[-0

,,-I-=-------

'+ C VI).+~Vl!- 3b)p-= ~b s~ l~

t'f,'-l

~4(t1~~) (n+'i) J

10. 2a2 -4a-126

11. 3x2 - 40x + 10012. 3n2 -60n+300

.2. ( t\ '=-.2a. - G 3)

P :::: ~oos=- -\jO3{n 'l-_2--0n + 100)

_ ~o) _102-( C\ _ q)[ ~ -\-1-) 3 (o-\o)l n-'01- 3~DX-I~OO~ X (x -\0) - \0 (x:-,0()(-IO) (3){-1~

3°v

C. Factor each trinomial com letel .

4. x2 -64 X r 0)( -6Cf 5. x2 -8x+12 -(,) - 2-

(:;z-g)CX+V C><-0(1.-9

pvo~J-:: - b

St..o.-vv1 :: 0

B. Solve.13. n2 + n - 90 = 0

(n+(O)(~-"') ;::0

n =- -10 ) n =- 4

14. 5n2-45n+90~0 ,"~-;

'5C~)=,O5(n-b)(n-~) -==0

Y)~b) n-::.~

15. n2 +4n-21 = 0 7-" -ILf

en +1jCn-~~O

n-=-'=t-j n=-.3

16. n2 +3n-70 = 0

0+ID)'n-1-)-== D

n :::-\0) n -::.q-

19.7n2+64n+9=0

p -==- ,) S ~~c.f h3}' "It'2.-

'=J-n + G>t1+n +q ==0

1-n(n+ q) + (t14c\) =D

CYl+'\) (:rn+0 ~D

01'\- I1/\- a' 1,---J' ---I ) =r-

17.3n3-15n2+12n=0 18 3 3 92. n - n -54n=0

3n (V\~-S-"+4-)=::0 3(dY\~-3n -l~)==O

, Y)ln - 4' ) In - \) ~ 0 '3n ( Yl - C ) en + '2.,) :;: 0

n -::::.-0) n ~ Lt') Y) = \ n:::-o) Y1~ b) n,:: - 3

20. 2f?+11n+14=0 't£?::: 2&' S~ 1\

7-)4 \\')...

.2\1 + 1-Y1 +4-.-1 +'4 ~o

Y\ (2. y\ +1-") +- '-~n1--:tJ =0

(2-n+1-)(n + I}.) ~O

V\- '+. V"I- C"')1'--<2-"'> ,,--~

Amwer Bunk for solrtoo DrobllllOO {lB- 21}.

11

n=O or n = 3n = 0 or n = 4n = 7 or n =-7n = -- orn = 0 or n = -n=Oorn=6

or n = 6or n = 1 77or n =-3n=-9

or n=9

7

3n = -10 or n = 7

n = -- orn = 3 or n = -10n=9 or n = -10n = 0 or n = --n = -7 or n = 32

2n =-2

or n = -10

lAlgebra 2 IAssignment: Factoring Special Cases

NamePeriod Date

Sum or Difference of Two Perfect Squares

1) x2 -100

(x+ Ib)(>C-IV)

2) x2 -81

()C -t- q){X - q)

5) x2 - i(K-KJ )(X-})

6) 9v2 -16z2

(3V +4-"2)( :S\/ -- 4-~)

8) 25a2 -100b2

2 ~ ( Cl 2- _ 4-h l..)

2-5 ( ct + 2- 6)[4 - 2b)

9) 64x2-1

(YX +-1 ) ( f )(- I)

Difference of Two Perfect Cubes

10) x3 27 11) x3 1,00012) x3 -125

()( ---s) (X2 +3x: -+ 4)

>(>_ , 0 3-X3_ 5.5

~ eX -10)( >< 2-+ 10)( +IO~

~ (x-~) Lx 2.+ S-X+2S

13)8x3 125/

14) 27x3 115) 343x3 - 64

( 2-X:}> - [5LJ ) ~

2-

.(2)x-l)( QX +3x+0

(TX.)3 _ Lf ~

'lt~

')..

(2)< - f;(j)( 4)( +/(»)I.(j f-2r

•=-('f)(- 4)( 4:1X -+ z.-f)(1

­'-

Sum of Two Perfect Cubes

16) i +8 17) x3 +64

( ~ -+2-)( ~ 7-_ '2-'t f If) 6<+ 1.+)(X "--Lf)( -+ Ib)

18) x3 +27'2--

(x-+~) eX -3X -f- &f)

Perfect Square Trinomials

~(;;33:8Y~• )~g (!LX 4)( Lf~ - 2)(~~

0° .~ . ~

(c..I'x~ 2-~){16')(- ry>((j+4-

_____ 1== ~(2-x+'1) (lfX~2-Yt:\ ~ +.2A-h + b1. :: (ct. +6) 'l.-

C1 ~ 2-et,t. + b'L -;: (tt _~) 1-22) x2 + lOx + 25 23)4x2-12x+924) 25x2 +40-,-y+ 16y2

\

Cx+s-) rv

'l--1-

(2x- 3) (5X+41.J)

25) 36x2 -12x + 1

26) x2 +6.\y+9/27) x2 -16x + 64'l,..---

'L.

(x- ~) L(bX -I)

(x+ 3~)

II

Solve the following.

28) X3 -4x = 0 29) x2 -4x =-430) 5x+6 = _x2

X( ,,7-_ 4) ~OX =-4K+tt ~ 0X' +5)C-t b -=- D

X LX -t 2.--)ex: - 2-) == 0

L y- 2.-J '2-- :::: 0Lx + f2,- ) L )( -+ ~) ==- 0

x- D) X==-_2-jX~lX= YiX--_2-j )L>l.J

Answer box for questions 1-9.

przme 25 (a + 2b )( a - 2b)(2a - 2b) ( 2a - 2b)(x+9)(x-9)przme

(8x-1)(8x +1)

(x+10)(x-1O)(7a+8b)(7a-8b)prime(4x+6)(4x-6)

prime

(3v+ 4z )(3v - 4z)(x+y)(x-y)(3a + 4b) (3a - 4b)(lOx -1)( x -10)

Answer box for questions 10-15.

prime(7x-4){49x' +28x+16)(x-5){x' +5x+25)(3x-1){9x' +3x+l)

(x-3){3x' +6x+27)

(x-3){x'+3x+9)(x-4){9x' +4x+16)prime

(7x-16)(7x' +28x+4)

(4x-25y){x' +lOOxy+5y')(x-10){x' +10x+lOO)(2x - 5y){ 4x' + 1O:xy+ 25/)

Answer box for questions 16-21.

prime (X-3)(X2 -6x+9)8 (2x + y) ( 4x2 - 2xy +i )(x+3y){x' +13x+9)prime

(2x+5){4x' -lOx+25)

(4X-2y)(4x2 -2xy+4l)(x+4){x' -4x+16)prune(4x+4)(4x' +8x+16)•

prime

(x+3){x' -3x+9)(x + 3) (X2 - 6x + 9)(y+2)(/-2y+4)X(x+l)(x2 -x+l)

Algebra 2 Name

Assignment: Factoring Mixed

PeriodIDate

qtwft/ {dV ~OtAl'. t}w1r "

1) 6x2y-3xy

J,Xi (2-)(-1 )

it{l HW.s lL?~~~ (k.'1 \-{w T eta).. Hw

2) 25a2 -35a 3) -12x2 +36x-60

'5q ( 5Ct -::r) -12.( X?-- 3 )t-rs-)

15) 2x2 -50

2-(}G ~-Z~)

2--( )( -t&-) ()(-~ )

13) x2 -13x+36

4) 64x6-1 5) 16n2 + 25m26) x4-l

:,) 2r 1-])YI'~~~+~v) C}G 2-_ d ~)(~X .- I

(iX:~t-')( fX~-I) .~ ["tt() C)(+~)C)C-~)( 2-X +\X Y-)( 1.-_ ~ -t 1)(2-)(- D (<IX -+ .,. '.) 7) 4x2 -81

??

8) 20x- + 40x + 20 9) x- +9

(2X+q) C 2-X-q)2-0 LX ~+2.>C+l )eriV}'\-L')....

2o( ><::+1)

10) a2 +8ab+16b2

@64a2-36b212) i - y+1

~.

2-(~({ +(~)(rCi ~t~)

(Ctt-4b) (Jy;l~/ ",1,,,1.,_ '?L\

17) 4x2 -8xy+4i

If ( 'tC "- '2-)('J tfJltCX-([)"l--

2 3 218)3x-y

?(~"::-!'>-)

3(Y:+(1)(>£-V

19) x6-64 20) 2a4 -16221) 10x2y-6xy-20xy2

(X'-r.\> )()(;-q)2( C{ ~ -g I )

2-X>1 C~)C -3 -lot)l)( tl.) (~2._2.)( +4-)C)(_1)(j(~2y+

V z ( '\ ~-t 4 ) ( q 1-_ 1j:Ll tt l,-ttt)(q + ~)(G\. - 022) / -8i +16

23) 21x2 - 42xy + 35y224) 16x2 -80x+lOO

L ~~Af .... 1- (~'i :-C'1C(j 1-S-a~)L.f elf JL ~ 2-o,)C + 2.-- s-)

(~ "+ 2..)'-- (';J .:...'2.-)

L{- ( Z-)t- r)~25) 18l-98y

26) 25i -4927) 33x2y+99x3l-121x2i

2-'}C'ld >-~ <1-'1)l \:tt- 't)(f"(1 -t)t1 )('l--d- ( 1+ 1x'~">--II~)

2-~(3~ +T)(3crr)

Answer Box

(a+4bt (X2 + /)(x+ y)(x- y)prime_12(X2 -3x+5)lb ~3, ,

25a(a-5)

(x+ y)2 (x+ y)(x- y)5a(5a-7)(8x' -9)(64x' +72x' +81)1-prime

tt3xy(2x -1) 20(x+ 1)'.4 ( 4a + 3b) ( 4a - 3b)"I g.•0;.,

(3a + 4b) (3a - 4b)

20(x+2)(x-2)2y(2xy -1)(2x + 9)( 2x - 9)::r

-4( 3x2 - 9x -15)

(a-2b )2prime

2(a2+9)(a+3)(a-3),'1--

2-D

(5y + 7)(5y -7).2-£

(y-2)'(y+2)'2Y(3;..+PC3Y -7)

(x+2)(x2 -2x+4)(x-2)(x2 +2x+4)~'2-

t 4

2( a2 +9)(a+3)

7(3x' -6xy+5y')2xy(5x-3-lOy)4(2x-5)2

1.->'2--1 7--'1

(x-9)(x-4) I~

2(x + 5)(x-5)llx'y(9xy' -lly+3)a2b(2b2 -7b + 4a)f~

2--:r1'1

3y(2x-3)(4x' +6x+9)

4(X_y)23(x+ y)(x- y)(2x -1)( 4x2 +2x +1)(2x +1)(4x2 - 2x +1)J (

11"l~ ~