Unit #3 – Polynomials MPM2D1

Progress Check

1. Simplify:

a) (5x2y3)2 b) (8x3y)(4x2y7) c) 5 8

3 2

100x y

5x y

2. Expand and simplify:

a) 4x(x – 3) – (3x – 5) + 3x(5 – 2x) b) 3x2y3(x3y + 5) – 4xy(3x2y – x4y3)

c) (2x + 1)(4x – 5) d) (3x – 4)2

The purpose of the progress check is to diagnose areas that you need more practice with before the test.

1. Review your notes before trying the questions in this package.

2. Answer the questions on this handout. Treat it like a test. DO NOT look at the answers until you have

finished all of the questions.

3. Use the answers provided to check and see how you did.

4. Go to the course website (http://sites.google.com/a/hdsb.ca/TAB-MPM2D1) if you need to see the

full worked out solutions (click on Unit #3).

5. Use the additional review questions provided in the textbook (see unit outline) to practice more

questions like the ones you had trouble with in this package.

6. Although this progress check contains a wide selection of questions from this unit, it does not cover

ALL of the possible questions from the unit.

e) 10x(x – 1)(3x + 1) f) (4x – 2)(4x + 2) – (x + 3)(x – 3)

3. Factor as fully as possible:

a) 3xy + 9x3y5 – 15x2y4 + 12x5y3 – 30x10 b) 4xy – 2x – 14yz + 7z

c) x2 + 5x – 6 d) 10x2 + 43x – 9

e) 3x2 – 10xy + 8y2 f) 4x2 + 14x + 12

g) x2 – 64 h) 200x2 – 32y2

4. For each of the following expressions, determine a value of k that makes each factorable. Factor the

expression to prove that it works.

a) x2 + 15x + k b) 3x2 – 14x + k

c) 5x2 + kx + 7 d) kx2 – 5x + 7

5. For a rectangle with sides x + 2 and x – 7:

a) Write and simplify an expression for the

area of the rectangle.

b) Write and simplify an expression for the

perimeter of the above triangle.

c) If x = 10 cm, calculate the actual value for the area and the perimeter.

6. The product of Jane, Harry, and Karl’s ages is shown by the expression 40x3 + 120x2 + 90x.

a) Determine an expression for each

person’s age, if Karl is the oldest and

Jane is the youngest.

b) What do the expressions from a) tell you

about Jane and Harry?

c) If the sum of their ages is 62, how old is each person?

7. Miss Pick drew a circle and a rectangle on a piece of paper. Using the information given, determine

the actual length of the rectangle that she drew.

Answers:

1a] 25x4y6 1b] 32x5y8 1c] 20x2y6 2a] -2x2 + 5 2b] 7x5y4 + 15x2y3 – 12x3y2 2c] 8x2 – 6x – 5 2d] 9x2 – 24x + 16

2e] 30x3 – 20x2 – 10x 2f] 15x2 + 5 3a] 3x(y + 3x2y5 – 5xy4 + 4x4y3 – 10x9) 3b] (2y – 1)(2x – 7z) 3c] (x – 1)(x + 6) 3d] (5x – 1)(2x + 9) 3e] (x – 2y)(3x – 4y) 3f] 2(x + 2)(2x + 3) 3g] (x – 8)(x + 8) 3g] 8(5x – 2y)(5x + 2y) 4a] k = 14, 26, 36, 44, 50, 54, 56, -16, -34, -52, …

4b] k = -17, -5, 11, 16, 15, 8, -24, -49, … 4c] k = 36, -36, 12, -12 4d] k = -38, -78, -2, -18, -48, -88, … 5a] A = x2 – 5x – 14 5b] P = 4x – 10

5c] A = 36 cm2, P = 30 cm 6a] Karl = 10x, Jane = 2x + 3, Harry = 2x + 3 6b] Same age 6c] Karl = 40, Harry = 11, Jane = 11 7] L = 15.75 units

Information

The area of the rectangle

is A = 10x2 – x – 21

The area of the circle is

A = 9πx2 – 30πx + 25π

The length of the

rectangle is bigger than

the width.

The rectangle and the

circle have the same

width.

So\r*ion sMPM2D1Unit #3 - Polynomials

Progress Check

simntfrha) (5xT)'

Expand and simpliff:

-/flf,.a) 4ir(x - 3) -(3x - 5) + 3x(5 - 2x)

= U'-JAL-U*S+l5x-dc'2t+ox+5=[t*AL-----

t) (sx3v)(+xY)

=F412oxa y

q

. l00x5v8c),t'r-

The purpose ofthe progress check is to diagnose areas that you need more practice with before the test.

l. Review your notes before tying the questions in this package.

2. Answer the questions on this handout. Treat it like a test. DO NOT look at the ensw€fii until you have

finished all ofthe questions.

3. Use the answers provided to check and see how you did.

4. Go to the course website (http://sites.google.com/a/hdsb.ca/TABMPM2D1) if you need to see the

full worked out solutions (click on Unit #3).

5. Use the additional review questions provided in the textbook (see unit outline) to practice more

questions like the ones you had trouble with in this package.

6. Although this progress check contains a wide selection of questions from this unit, it does not cover

ALL of the possible questions from the unit.

t.

c)(

8x"- bK- 5gX.- 2rtX+ ltl

= 3x5\\ + tsx\3- l2x3v"+ txE

-T

a

-r -

= Bf- IOX + \x-5= Qx"- lzx -tzx + t (o

e)/-\l0x(i- 1)(3x+ 1)

\=-.:

lox fg*"+x-3x - l]lox (3K'-2x- D30K3- 20xa- lox

A\n lr4x - tgr) -k* + 3)(x - 3)

{(uf' Bx-t*At (x1axr3x -e)=l(rbxz-t) - t'Cx.-q)

= tlfi-+ :I"+g=l]sx'*5:1

----

- 1ox2

d) t#*or)'s'19*91= Zx(sx- D + 1(ex- r)

3. Factor as firlly as possible:

:tni.c) x2 + 5x-6

= Xz{ f !I_-6-

- -r-f

---

1n4..'e) 3x2 - lOxy + 8y'z

= nF41--1ry-8f

(5x-DCzr+9

D q* + t4x+ t2

= 2 (zx"+lx+ b)=Z[rf1U+3x+to]

-to*;,{Xy

-l5xf+t 4xv _ 2*_ l{y7+ 7z|#t i-.-l

zx(zy-) az(z

= x(x-D 16&

'l0q

= z [zx(x*D *Ecxtzl

{r\Xe) *-eq

x2 tOx-b Lf

= K".?xt8x -btt

= x(X-t)+r(x-8)(x-8XKtr)

h) zoo*-zzf @@\ -%f,= 8 (zsxt- \f) \

= 8(zsx.-s/Ut,rf)= 8 [ox(rx-zy) +2,1(sx-zp]

8 (5x-zy)Ga*zy)

4. For each of the following expressions, detemrine a value of k that makes each factorable. Factor theexpression to prove that it works.

I Ka) x2+l5x+k \ ,/=X2+l5x+ru l,N't= X'+ tx+ l{rJt,t / t5 \= X(Xrt) +lll[t+ D ,l K = lT=ffi It<=rT\

Otirer Ophons:(= 26rbb, $,5o,5t't, 5b

-lbl -3tt f62, .. .

b) 3x2- l4x+k

= 3xz- lTx - tJ= 3f $x -tJx- tJ

o'f'lner oph'ons:I\=-5t tiltbl \b,1

ooo

O kx2 -5x+7-tzx15x+7

x'.el 17

3k =51l(=- l'1

8,-2\ in

),l ,.?

lLt -8tK= -lZ

c) 5x2+k+7

' 5f + SbxtJ

= 5x1lx+35t+7=xCFx+D+-l(4*D f(s 3b

5x+DCx+t

otlner od\onsK = -3b, lzr'l1

Otlrer oP+ions:

\ui = -38 )-1 8,-2r- 18, -\8,_$gl. .

= 3x (xtD -17(xt)

. -t2x2- lDt t 1x+1

= -lXX+Dt'l&+j

A = xt-sx-lT P= Ltx- lo

c) If x : l0 cm, calculate the actual value for the area and the perimeter.

fi= (ro)z-Scro)-lT ! = rfcro)- lo

? = \o-LOft = loo -5O,-ltA = 3Lo ct-Z ?:3C) crrr

.: Tlre qreA iS 31, crtrz qnA utlne ?ecirneter fS ?O crn,6. The product of Jane, Harry, and Kad's ages is shown by the expression 40x3 + tZD* + 90x.

a) Determine an expression for each b) What do the expressions from a) tell youabout Jane and Harry?person's age, if Karl is the oldest and

Jane is the youngest. 3bt

5. For a rectangle with sides x + 2 andx- 7:

a) Write and simpliff an expression for thearea of the rectangle.

A= L\^f[ = (x+z)Cx-])A = xz-JK +*.- ltl

= lo x izxCat3) + 3tCzr+a)]x (Zx+3XZx+a

Ko{1oxr Sone'2;.13, Har =N+3") If the sum-of ffieir agesls 62, how 1S personl

!O.x + ?-f+3+ ?r+7= 62l{x+b = 62

b) Write and simpliS an expression for theperimeter of the above triangle.

! = 2L+ zuf! = 2&+2) +2(.X-'?)n=?X+$+Ac-tT

, lox [t*.+6x+trr+il= tox (trt* tzx *q)[i1'-1.i1::-!i" "X'

ondt'lne*c"

l4qrl = to C{)

= Llo

Harry

Trrng = 2Cut)+33 gf3= ll

Joneare

K+2

lLtL156Kor\ 16 TO )ears o\lqnd Tane old rytry qre

7. Miss Pick drew a circle and a rectangle on a piece of paper. Using the information given, determinethe actual length of the rectangle that she drew.

Inforrration

The area of the rectangleis A: 10x2 - x-21

The area of the circle isA=9zrx2-30nx +25n

The length of therectangle is bigger thanthe width.

The rectangle and thecircle have the same

width.

\--'---'lt^)

ft = [ox"- Y-zl: loxz- lSx * lltx-Z l

= 5x(at-3) +?Ox-D

= Ox-3)(srtr)

C;rc\t\jlArr-A-.

fi =qTT f-3dk +"b\='ff (9x2-3ox +25>

N id\ln = ld id*'l^

7':tL-] = z(bx-5)7N.-7 = LoX- lO

-b = LtX- lO-l = \X

+=X1,15={

[= 5(r.-l s)rJL = 8,15+7L = 15.15

=fr (lx1 t5x-r5x+2t= I [ax(rx+) -b(3x;n: l[ (ax-S)(3x-s)= T[ (3X-5)'

t. -lh€, \.no1'il" i s

l5'1d *nils'