What Happened When the Boarding House Blew Up?

Factor each trinomial below. Find one of the factors in each column of binomials. Notice the letter next to one factor and the number next to the other. Write the letter in the box at the bottom of the page that contains the matching number.

3x2+7x+2

2x2+5x+3

3x2 - 16x + 5

0 7x2 - 9x + 2

® 6u2 + 5u + 1

0 8u2 - 9u+ 1

0 10u2 + 17u+ 3

® 9u2 - 9u + 2

0 5u2+11u+6

3n2 + 2n - 1

5n2 - 4n - 1

2n2 + 5n - 3

7n2 - 13n - 2

0 3t2 + 14t - 5

4t2-11t+7

() 6t2 + 5t - 1

0 3t2 - 20t - 7

0 (5u + 3)

(x - 1)

0 (3x + 1)

0 (3u - 1)

® (2u + 3)

• (x + 1)

0 (5u + 6)

• (2u+ 1)

0 (3x - 1)

0 (u - 1)

0 (3t - 1)

0 (n - 1)

• (3t + 1)

0 (n - 2)

• (t + 1)

0 (3n - 1)

CI (2n - 1)

• (3t - 7)

• (4t - 7)

OY (3u - 2) (x - 5)

® (8u - 1)

(7x - 2)

(5u + 1)

(x + 2)

(7x + 2)

(2x + 3)

(u + 1)

(3u + 1)

ON (n + 3)

® (t - 1)

• (2t + 1)

OO (n + 1)

OF (t+ 5)

(5n + 1)

(t-7)

® (7n + 1)

(6t - 1)

1

2 3 4

5 6 7 8 9 1 0 1 1 12 13 14 15 16 17 1

OBJECTIVE 3—o: To factor trinomials of the form axe + bx + c, where a is a positive integer greater than 1.

ALGEBRA WITH PIZZAZZ! © Creative Publications 91

co0 2x2 — 21x + 40 0 3m2 — m — 30

TH

(4m — 9)

AT

(3x + 1)

PA

(m — 2)

DO

(m — 3)

NE

(2x — 5)

XT

(3m — 10)

CK

(14m — 11)

YO

(2m — 3)

UR

(5x + 1)

UP

(6x + 1)

UW

(15m + 1)

IN

(x + 3)

PL

(m + 2)

AN

(x + 4)

DA

(5m + 3)

RE

(x — 2)

MA ,

(3m + 2)TT

(9x + 2)

CO

(7x + 8)

LD

(3x + 4)

IB

(7x + 2) (8m

ER

+ 3 (m

AJ

+ 3) (7m

ET

+ 2) (x

ON

— 8)

HI

m — 1

GH

1)

-0

%/t--1-A:r 17117 IA Z.LAN)Gr %/kf' N) 1•4P-), Z1A\)Gf

OD

Gfc2IN)Gr 1•4e9U-Nrroesc-IN) GI Ik/VIN)Gr IN Q r CD m Factor each trinomial below. Find both factors in the rectangle below and

cross out each box containing a factor. You will cross out two boxes for each

13

CD > exercise. When you finish, print the letters from the remaining boxes in the co_ squares at the bottom of the page. sa)

N

N 1• O 6x2+ 19x + 3 ® 15m2 + 19m + 6

5x2 — 9x — 2 0 8m2 — 5m — 3

® 9x2 + 15x + 4

0 4m2 _17m+ 18

0 14m2 + 17m — 22

0 co

- ® 7x2 + x — 8

4n2 — 49

17 2 ± 8n + 12

n2 — 9n + 20

fl2 + 16n + 64

n2 + 2n— 15

3n2 — 8n + 5

(u+ 3)

OM (u + 1)

@ (2u + 9) ® (2u + 1)

(u — 3) © (8u + 3)

® (5u — 2) ® (2u — 1)

® (3u — 14) (u —7)

(u+ 2) ® (u — 2)

© (3u + 10) (5u — 2)

OBJECTIVE 3—p: To factor polynomials using the methods on preceding pages (review).

ALGEBRA WITH PIZZAZZ! © Creative Publications 93

How Can Fishermen Save Gas ? Factor each polynomial below. Find one of the factors in each column of binomials. Notice the letter next to one factor and the number next to the other. Write the letter in the box at the bottom of the page that contains the matching number.

0 (n + 1) OO (n — 3)

0 (n + 2)

@ (2n — 7)

• (n + 8)

® (n — 5)

® (2n + 7)

(3n — 5)

0 (n + 5) 0 (n + 8)

• (n — 1)

OK (3n — 1)

• (n — 4)

OA (n + 6)

*&+:.!+&+&+&*&+/Zk)&+&+k)W&WW1 4&&&+&kl+/14+&,&+&+ .+&+k)WWW &&+ ,4+&+&+& +&&

a2 + 4a — 21

0 5a 2 + 9a — 2

0 2a2 + 11a + 15

0 1 — 9a4

0 a2 — 11a + 30

10a 2 — 3a — 1

• (a — 5)

@ (a + 7)

0 (5a + 1)

O (a + 2)

@ (a — 1)

0 (1 — 3a2)

(2a + 5)

® (2a + 1)

® (a— 6)

0 (a — 3)

© (a + 3)

O (5a — 1)

® (2a — 1)

ON (1 + 3a2)

&&+&+&+&WW+ 4.+(Z/WW&Ikfk+&+&.+&+&+&+&+k &+k+WZ,W+(-4+(44WWWW&WW&.+&+&Wv-Z/fkif&

13 1 8u2 + 19u + 6

0 25u2 — 20u + 4

3u2 — 11u — 14

u2 — 4u — 21

0 6u2 + 17u — 10

2u2 + 5u — 18

1

2

3

4

5

6

7

8

9 1 0 11 12 13 14 15 16 17 18

What Do You Call a Sore on a Police Officer's Foot ?

Factor completely each polynomial below. Find your answer and notice the letter next to it. Write this letter-in the box containing the number of that exercise.

0

O O O O O O O O O O 0

3x2 — 15x + 18 x3 + 11x2 + 10x 8x3 — 18x 5x3 — 40x2 + 60x ( ( 4x2 + 8x — 60

( 2x3 — 20x2 — 48x

(Answers:

0 5x(x + 3)(x — 4)

ON 2x(2x + 3)(2x — 3) 0 2x(x + 6)(x — 4) © 3(x — 2)(x — 3) © 4(x + 5)(x — 3) OA x(x + 5)(x + 3) ® 4(x + 5)(x — 1) 0 x(x + 10)(x + 1) • 2x(x — 12)(x + 2) • 5x(x — 2)(x — 6) ® 2x(4x + 9)(x + 1)

4m2 — 18m + 14 15m3 + 24m2 + 9m 15m2 — 10m — 25 50m3 — 2m 3m 2 — 10m + 8 60m3 + 54m 2 — 6m

Answers: 3m(5m + 3)(m + 1) 5(3m + 1)(m — 5) (3m — 4)(m — 2) 2(2m + 1)(m + 7)

5(3m — 5)(m + 1) 6m(5m — 1)(2m — 1) 3m(5m + 2)(m — 1) 2(2m — 7)(m — 1) 2m(5m + 1)(5m — 1) 6m(10m — 1)(m + 1) (3m — 2)(m + 4)

( (

5 8 11 7 1 3 9 6 2 12 4 1 0

ALGEBRA WITH PIZZAZZ! 94 © Creative Publications

OBJECTIVE 3—q: To factor polynomials completely (excludes factoring by grouping).

2x2 + 22x + 36

5x3 — 10x2 — 40x

18x3 — 98x

axe — 7ax + 12a

x4 + 8x3 — 20x2

3x2 + 13x + 10

10x3 — 25x2 — 35x

12u2 — 28u — 24

u4 — 3u2 — 4

15u4 + 2u3 — u2

2u2v — 1 8uv + 28v

12u3 + 36u2 + 27u

40u2 + 15u — 55

u4 — 10u2 + 9

Answers for 8-14:

u2 (5u — 1)(3u + 1)

3u(4u + 3)(u + 3)

(u + 1)(u — 1)(u + 3)(u — 3)

2v(u — 7)(u — 2) 4(3u + 6)(u — 1)

(u2 + 9)(u + 1)(u — 2)

`4(3u + 2)(u — 3)

u2(15u + 1)(u — 1)

5(8u + 11)(u — 1)

2v(u + 14)(u + 1)

(u2 + 1)(u + 2)(u — 2)

5(4u + 11)(2u + 1)

3u(2u + 3)2

0 w

m 0 H m

H 0

0 0

-0 0

0 C. (-) 0 3 0 CD cT

CD X

0 co

iv 0

0

o

co 0 -0.

> • r-

0 m

@Co

2>

N

O N (7, N

CD

Old Lawyers Never Die, They Just

14 12 5 4 1 10 4 7 9 2 13 13 4 2 14

Old Skiers Never Die, They Just

8 12 3 12 6 11 10 7 14 14

YOU MAY HAVE HEARD THAT OLD MATH TEACHERS NEVER DIE, THEY JUST REDUCE TO LOWEST TERMS. TO FIND OUT WHAT HAPPENS TO OLD LAWYERS AND SKIERS, FOLLOW THESE DIRECTIONS: Factor completely each polynomial below. Find your answer in the appropriate answer column and notice the letter next to it. Each time the exercise number appears in the code, write this letter above it.

Answers for 1-7:

(3x + 5)(x — 2)

5x(2x — 7)(x + 1)

2(x + 2)(x + 9)

a(x + 6)(x + 2)

x2 (x + 10)(x — 2)

2x(3x + 7)(3x — 7)

x2 (x + 4)(x — 5)

2(x + 3)(x + 6)

5x(x — 4)(x + 2)

2x(9x — 7)(x + 7) (3x + 10)(x + 1)

5x(2x — 1)(x + 7)

O a(x — 3)(x — 4)

Answers for A-G:

(2b - 3)(r + 4) HUNTED

(5c - d)(2c - d) WHEN

(x + 3)(x - 2) THE

(a + 2)(5a - 2) HE

(x2 + 1)(k + 4) BEAR

(k2 - 7)(x + 3) THE

(a + 2)(2a + 5) MAN

(k - 2)(x + 3) DEER

(n - 5)(3n - 1) WHO

(2b + 4)(r - 3) SHOT

(5c - d)(2c + 4d) UNTIL

Answers for H-N:

(6 - h)(x3 - 4) MISS

(5t2 - 1 )(t + 7)

MADE (6h - 1)(x3 - 4)

ON (a - 2b)(5a + 3b)

BEAR (2d + 1)(5 - n2)

RANGER (a - 2b)(3a - 5b)

PUT (w2 + 1)(3w - 1)

FOREST (2d - 5)(5 — n2)

SHOOT (3u2 - v2)(u2 + v2)

HIM (y2 + 3)2

CLOTHES (u2 + 3v2)(u2 + v2)

A96 ALGEBRA WITH PIZZAZZ!

© Creative PublicationsOBJECTIVE 3—r: To factor a polynomial whose

terms contain a common binomial factor.

Did You Hear About... A B C D E

F G H I J

K L M N? ? ?

Factor each expression below. Find your answer in the appropriate answer column and notice the word beneath it. Write this word in the box containing the letter of that exercise. Keep working and you'll hear what's "bruin."

OA x(x - 2) + 3(x - 2) ® a(2a + 5) + 2(2a + 5)

n(3n - 1) - 5(3n - 1) ® 2b(r + 4) - 3(r + 4) ® (x2 + 1)k + (x2 + 1)4 OF (5c - d)(2c) + (5c - d)(4d)

® k2(x + 3) - 7(x + 3) 0 w2(3w - 1) + (3w - 1) 0 2d(5 - n2) + (5 - n2) ® 5t2(t + 7) - (t + 7)

0 3u2(u2 + v2) - v2 (u2 + v2)

® (a - 2b)3a - (a - 2b)5b

0 6h(x3 - 4) - (x3 - 4)

ON + 3)y2 3(y2 + 3)