(ev
tinit 5 - Folynomials
represents
an
1. A largewhitesquare
a 1-tile.
whitesquarerepresents
represent -x-tile,anda small
, a blackrectangle
represented
bythisset of algebra
tiles.
Writethe polynomial
b' -3x2+ 3x+5
a . 3 x 2- x 3 + 5
3x2-3x+5
d.
3x- 3x2+ 5
tiles.
setof algebra
bythesame
thepolynomials
thatcanberepresented
2. ldentify
i) 3x2- 2+ 6x
ii) 3x2- 6x+2
iii) -2+ 6x- 3x2
i v ) 6 x -2 + 3 x 2
a. iii andiv
i andiv
c. ii andiv
d . i a n di i
3. ldentifythepolynomial
that is equivalentto4 - 6v-'.,v2.
i\
ii)
7v2+ 6v- 4
4+'7v2-6v
-'7v2.- 6v + 4
iv) -'lv2 -4+6v
iii)
a, tv
b. ii
c.
l
llt
4 . S i m p l i fly0:x 2 - 8 + 3 x + 5- 6 x 2- 6 x
c' 4x2+3x+3
d. 4x4-3x2-3
a' 4x2-3x+3
4x2-3x-3
5 . Add: (8x- 6)+ (-4x- 2)
4x-8
b. 4x-4
c. t2x- 8
d.4x+4
form'
in simplest
of thistriangleasa polynomial
6. Writethe perimeter
g ) + ( K x +r o )
? - - t o , , - t) r ( { x - J'lx- - I
a. 21x-24
T-lx-4
c' 21x+24
b. 27x+4
7. Alargeblacksquarerepresentsa-xt-tileandablackrectanglerepresentsa-x-tile'Writethesubtraction
tilesrepresent'
thatthesealgebra
sentence
a
b, ?3r2-zx)-(zf -zx)
(3x'1x2+2)
8. Subtract:
23x-7
F" -11x+
h. -1 lx2- 9x- 3
i
c. (-2xt -2x)- (-3x'-3x)
(3^2 -:x) - (-zx2- 2x)
a. ?2^2- 3x)- (-3r2- 2x)
xz+Slsx)
- l l x z - 3 x+ 7
llxz + 3x-'l
an-x-tile'anda
represents
represents,-"'til", a blackrectangle
9. A largeblacksquare
a 1-tile'
squarerepresents
smallwhite
Whatisthedivisionsentencemodel|edbythissetofa|gebratiles?
trtrtr
-lt"-)xtU
EtrDtr
-32x+ 16
a. -32x2
-2x2-2x+6
-32x?
+32x+48 d'
16
2x2-2x+6
/
1 - 0A. l a r g e w h i t e s q u a r e r e p r e s e n t s a n x ' - t i l e , a w h i t e r e c t a n g l e r e p r e s e n t s a n x - t i l e , a n d a
a 1-tile.
smallwhitesquarerepresents
tilesbelow?
multiplication
is modelledbythealgebra
sentences
Whichof these
2x(2x+5)
i)
ii) 2Qx2+ 5)
iii) x(2x+5)
iv)
2x(4x2+ l0r)
2{rS
r--l r---'r tr t r t r t r t r
nI [ [ [ [ [ [
9'r- Lr
n
U n I I m [ [
@.) iii
d. iv
b. ii
-!2x2
11. Divide:---;3x'
a. -4x
b. -9x
-4c(2c- 3)
12. Multiply:
a' -Zc2+'7
b. -gc?- 3
d. -9
-4
c'
-.Bcz
- 12c
-8c2 + 12c
-tnp
. -zop2
is, Divicie:
--
- a n'2-
a. 5p2- rcp
5p+4
c. 8op2
- a+
d, 5P+4P
3x2- 4x- 9? A
thepolynomial
tileswouldyouuseto model
14. whatalgebra
@ A
lfl [ I]oo""oo
15.
J.O.
a -xt-tile,a whiterectangle
an xt-tile,a largeblacksquarerepresents
squarerepresents
A largewhite
-x-tile.
a
represents
anx-tile,anda blackrectangle
represents
polynomial,
Writeihesimplified
Jffi
tilesto subtract:
t-7. usealgebra
fix2 - o)t(4x2 t I lr;3)
w@
[] ll rl
WA
'- 1-\t'otr
aff t
frlcs'
Do D o D D
= 3 r a r -t r " - ?
C I i l 0 $ 0 0 6[00U
ooo
oDo
p
nrl
t
tilesto multiply:S(-Zx2- S)
L8. Usealgebra
- lOr]- Jf
. F l - d.
D,D\
D- -a
v
i-P !
o o tP\
tilesto divide:$5d2- i24 * [-3)
19.Usealgebra
D t
-5c\t
+ "1d
for the followingquestion:
solution
in
this
student's
errors
the
20. ldentify
0
t@ @ f 9 r€ i=rcfln
D
t s @@ i B t-6,= r=flr=
@ @ @ i atd r= L:lclc:
(8x2- lox- 2)* [-2)
D
8x2 ,- lox, ,-2,
= --; + (--;)
+ (-J
-z
-z
-l
s
=-4* +
= -4x2-
-1r?+
5x + |
anx-tile,anda small
represents
anXt-tile,a white rectangle
2L. A largewhitesquarerepresents
w h i t e s q u a r e r e p r e s e n t s a lW
- t irliet e. a d i v i s i o n s e n t e n c e t h a t i s m o d e l l e d b y t h e s e a l g e b r a t i l e s '
n n n n E
A
H
U
E
nn[[[[[
nn[il[[[
Lt.,.-a+ lO >c
h+5
Jr
anx-tile,a blackrectangle
represents
a -xt-tile,a white rectangle
squarerepresents
22. A largeblack
sentencethat is
a l-tile. Writethe multiplication
a -x-tile,anda smallwhitesquarerepresents
represents
tiles.
bythesealgebra
modelled
l'to(-'c+t)
' - A*t*
2r'
tilesto add:(3x2- 4x)+ (3x2+ 8x- 12)
23. Usealgebra
- al asfollows:
added(8x2-6x+ t3)+(-13x+Ox2
24.Astudent
= ! 4 x 2+ ? x +5
wherethestudentmadeanyerrorsandwritethecorrect
work correct?lf not,explain
lsthe student's
answer