Question 1

Solve the problem.
-In a sports league of  n\mathrm{n}n  teams in which each team plays every other team twice, the total number  N\mathrm{N}N  of games to be played is given by  N=n2−n\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}N=n2−n . How many teams are in a softball league if the total number of games played is 110 ?

Accepted Answer

A)   10
B)   11
C)   9
D)   12

Question 2

Factor.
- 2x3+6x2−20x2 x^{3}+6 x^{2}-20 x2x3+6x2−20x

Accepted Answer

A)    2x(x−2) (x+5) 2 x(x-2) (x+5) 2x(x−2) (x+5)  
B)   Prime
C)    2x(x+2) (x−5) 2 x(x+2) (x-5) 2x(x+2) (x−5)  
D)    (2x2+4x) (x−5) \left(2 x^{2}+4 x\right) (x-5) (2x2+4x) (x−5)

Question 3

Solve the problem.
-A rectangular garden is three times as long as it is wide. If the area of the garden is  768ft2768 \mathrm{ft}^{2}768ft2 , find the length and width of the garden.

Accepted Answer

A)   length:  45ft45 \mathrm{ft}45ft ; width:  15ft15 \mathrm{ft}15ft 
B)   length:  256ft256 \mathrm{ft}256ft ; width:  3ft3 \mathrm{ft}3ft 
C)   length:  48ft48 \mathrm{ft}48ft ; width:  16ft16 \mathrm{ft}16ft 
D)   length:  16ft16 \mathrm{ft}16ft ; width:  163ft\frac{16}{3} \mathrm{ft}316​ft

Question 4

Factor completely.
- 4x2−814 x^{2}-814x2−81

Accepted Answer

A)   Prime
B)    (2x−9) 2(2 x-9) ^{2}(2x−9) 2 
C)    (2x+9) 2(2 x+9) ^{2}(2x+9) 2 
D)    (2x+9) (2x−9) (2 x+9) (2 x-9) (2x+9) (2x−9)

Question 5

Factor.
- 10z2−7z−1210 z^{2}-7 z-1210z2−7z−12

Accepted Answer

A)    (2z−3) (5z+4) (2 z-3) (5 z+4) (2z−3) (5z+4)  
B)    (10z−3) (z+4) (10 z-3) (z+4) (10z−3) (z+4)  
C)    (2z+3) (5z−4) (2 z+3) (5 z-4) (2z+3) (5z−4)  
D)   Prime

Question 6

Solve.
-Use the following graph to solve  x2+2x−15=0x^{2}+2 x-15=0x2+2x−15=0 .
Y = x2 + 2x - 15
2 + 2x - 15   A)   -3,5  B)   -5,3  C)  3,5 D)   -5,-3" class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

A)    −3,5-3,5−3,5 
B)    −5,3-5,3−5,3 
C)   3,5
D)    −5,−3-5,-3−5,−3

Question 7

Factor completely.
- 4 m2−944 \mathrm{~m}^{2}-\frac{9}{4}4 m2−49​

Accepted Answer

A)    (2 m−32) 2\left(2 \mathrm{~m}-\frac{3}{2}\right) ^{2}(2 m−23​) 2 
B)    (2m+32) (2m−32) \left(2 m+\frac{3}{2}\right) \left(2 m-\frac{3}{2}\right) (2m+23​) (2m−23​)  
C)    (2 m+32) 2\left(2 \mathrm{~m}+\frac{3}{2}\right) ^{2}(2 m+23​) 2 
D)   Prime

Question 8

Factor.
- 6x2−13xy+6y26 x^{2}-13 x y+6 y^{2}6x2−13xy+6y2

Accepted Answer

A)    (6x+3y) (x+2y) (6 x+3 y) (x+2 y) (6x+3y) (x+2y)  
B)    (2x+3y) (3x+2y) (2 x+3 y) (3 x+2 y) (2x+3y) (3x+2y)  
C)    (2x−3y) (3x−2y) (2 x-3 y) (3 x-2 y) (2x−3y) (3x−2y)  
D)    (2x+3y) (3x−2y) (2 x+3 y) (3 x-2 y) (2x+3y) (3x−2y)

Question 9

Solve the problem.
-The product of two consecutive integers is 11 more than their sum. Find the integers.

Accepted Answer

A)   -3 and -2
B)   4 and 5
C)   4,5 or  −3,−2-3,-2−3,−2 
D)   3,4 or  −3,−2-3,-2−3,−2

Question 10

Factor completely.
- 128x2−50128 x^{2}-50128x2−50

Accepted Answer

A)    (8x+5) (16x−10) (8 x+5) (16 x-10) (8x+5) (16x−10)  
B)    2(8x−5) 22(8 x-5) ^{2}2(8x−5) 2 
C)    2(8x+5) (8x−5) 2(8 x+5) (8 x-5) 2(8x+5) (8x−5)  
D)    (16x+10) (8x−5) (16 x+10) (8 x-5) (16x+10) (8x−5)

Question 11

Solve the problem.
-A long-distance runner runs 2 miles south and then 4 miles east. How far is the runner from the starting point? Round to nearest tenth.

Accepted Answer

A)    2.5mi2.5 \mathrm{mi}2.5mi 
B)    1.5mi1.5 \mathrm{mi}1.5mi 
C)    4.5mi4.5 \mathrm{mi}4.5mi 
D)    1.1mi1.1 \mathrm{mi}1.1mi

Question 12

Factor.
- t(8−m) +s(8−m) \mathfrak{t}(8-\mathrm{m}) +\mathrm{s}(8-\mathrm{m}) t(8−m) +s(8−m)

Accepted Answer

A)    t(8−m) +s\mathrm{t}(8-\mathrm{m}) +\mathrm{s}t(8−m) +s 
B)   No common factor
C)    (t−s) (8−m) (\mathrm{t}-\mathrm{s}) (8-\mathrm{m}) (t−s) (8−m)  
D)    (t+s) (8−m) (\mathrm{t}+\mathrm{s}) (8-\mathrm{m}) (t+s) (8−m)

Question 13

Factor.
- 4x2−5x+94 x^{2}-5 x+94x2−5x+9

Accepted Answer

A)    (4x−9) (x−1) (4 x-9) (x-1) (4x−9) (x−1)  
B)    (4x−1) (x−9) (4 x-1) (x-9) (4x−1) (x−9)  
C)   Prime
D)    (2x−9) (2x−1) (2 x-9) (2 x-1) (2x−9) (2x−1)

Question 14

Factor.
- t2+1.4t+0.49t^{2}+1.4 t+0.49t2+1.4t+0.49

Accepted Answer

A)    (t2+0.7) 2\left(t^{2}+0.7\right) ^{2}(t2+0.7) 2 
B)    (t+1.4) 2(t+1.4) ^{2}(t+1.4) 2 
C)    (t+0.7) 2(t+0.7) ^{2}(t+0.7) 2 
D)    t(t+1.4) t(t+1.4) t(t+1.4)

Question 15

Solve the problem.
-The height of a triangle is  4 cm4 \mathrm{~cm}4 cm  more than the length of the base. If the area of the triangle is  126 cm2126 \mathrm{~cm}^{2}126 cm2 , find the height and length of the base.

Accepted Answer

A)   height:  14 cm14 \mathrm{~cm}14 cm ; base:  10 cm10 \mathrm{~cm}10 cm 
B)   height:  19 cm19 \mathrm{~cm}19 cm ; base:  13 cm13 \mathrm{~cm}13 cm 
C)   height:  18 cm18 \mathrm{~cm}18 cm ; base:  14 cm14 \mathrm{~cm}14 cm 
D)   height:  17 cm17 \mathrm{~cm}17 cm ; base:  13 cm13 \mathrm{~cm}13 cm

Question 16

Factor completely.
- x10+32x5+256x^{10}+32 x^{5}+256x10+32x5+256

Accepted Answer

A)    (x5−16) 2\left(x^{5}-16\right) ^{2}(x5−16) 2 
B)   Prime
C)    (x5+16) 2\left(x^{5}+16\right) ^{2}(x5+16) 2 
D)    (x5+16) (x5−16) \left(x^{5}+16\right) \left(x^{5}-16\right) (x5+16) (x5−16)

Question 17

Factor completely.
- x2+20x+100x^{2}+20 x+100x2+20x+100

Accepted Answer

A)   Prime
B)    (x+10) (x−10) (x+10) (x-10) (x+10) (x−10)  
C)    (x+10) 2(x+10) ^{2}(x+10) 2 
D)    (x−10) 2(x-10) ^{2}(x−10) 2

Question 18

Factor.
- x2+4xy−21y2x^{2}+4 x y-21 y^{2}x2+4xy−21y2

Accepted Answer

A)    (x−7y) (x+y) (x-7 y) (x+y) (x−7y) (x+y)  
B)    (x+7y) (x−3y) (x+7 y) (x-3 y) (x+7y) (x−3y)  
C)    (x−7y) (x+3y) (x-7 y) (x+3 y) (x−7y) (x+3y)  
D)    (x−y) (x+3y) (x-y) (x+3 y) (x−y) (x+3y)

Question 19

Factor.
- 6x2+5xt−6t26 x^{2}+5 x t-6 t^{2}6x2+5xt−6t2

Accepted Answer

A)   Prime
B)    (2x+3t) (3x−2t) (2 x+3 t) (3 x-2 t) (2x+3t) (3x−2t)  
C)    (6x+3t) (x−2t) (6 x+3 t) (x-2 t) (6x+3t) (x−2t)  
D)    (2x−3t) (3x+2t) (2 x-3 t) (3 x+2 t) (2x−3t) (3x+2t)

Question 20

Solve the problem.
-A number is 12 less than its square. Find all such numbers.

Accepted Answer

A)   -3 and 3
B)   -3 and 4
C)   -4 and 4
D)   -4 and 3

Exam 11: Polynomials: Factoring

Factor. - $4 x^{2}-5 x+9$

Correct Answer
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Factor. - $x^{2}+4 x y-21 y^{2}$

Correct Answer
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Factor completely. - $4 \mathrm{~m}^{2}-\frac{9}{4}$

Correct Answer
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Solve. -Use the following graph to solve $x^{2}+2 x-15=0$ . Y = x² + 2x - 15 $Solve. -Use the following graph to solve x^{2}+2 x-15=0 . Y = x<sup>2</sup> + 2x - 15 A) -3,5 B) -5,3 C) 3,5 D) -5,-3$

Correct Answer
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Factor completely. - $x^{2}+20 x+100$

Correct Answer
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Factor completely. - $4 x^{2}-81$

Correct Answer
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Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is $768 \mathrm{ft}^{2}$ , find the length and width of the garden.

Correct Answer
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Factor completely. - $128 x^{2}-50$

Correct Answer
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Solve the problem. -The product of two consecutive integers is 11 more than their sum. Find the integers.

Correct Answer
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Factor. - $6 x^{2}+5 x t-6 t^{2}$

Correct Answer
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Correct Answer
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Solve the problem. -In a sports league of $\mathrm{n}$ teams in which each team plays every other team twice, the total number $\mathrm{N}$ of games to be played is given by $\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}$ . How many teams are in a softball league if the total number of games played is 110 ?

Correct Answer
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Factor. - $6 x^{2}-13 x y+6 y^{2}$

Correct Answer
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Factor. - $2 x^{3}+6 x^{2}-20 x$

Correct Answer
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Factor. - $\mathfrak{t}(8-\mathrm{m}) +\mathrm{s}(8-\mathrm{m})$

Correct Answer
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Factor. - $t^{2}+1.4 t+0.49$

Correct Answer
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Factor completely. - $x^{10}+32 x^{5}+256$

Correct Answer
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Factor. - $10 z^{2}-7 z-12$

Correct Answer
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Solve the problem. -The height of a triangle is $4 \mathrm{~cm}$ more than the length of the base. If the area of the triangle is $126 \mathrm{~cm}^{2}$ , find the height and length of the base.

Correct Answer
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Solve the problem. -A number is 12 less than its square. Find all such numbers.

Correct Answer
verified

Exam 11: Polynomials: Factoring

Factor. - 4x2−5x+94 x^{2}-5 x+94x2−5x+9

Correct AnswerverifiedShow Answer

Factor. - x2+4xy−21y2x^{2}+4 x y-21 y^{2}x2+4xy−21y2

Correct AnswerverifiedShow Answer

Factor completely. - 4 m2−944 \mathrm{~m}^{2}-\frac{9}{4}4 m2−49​

Correct AnswerverifiedShow Answer

Solve. -Use the following graph to solve x2+2x−15=0x^{2}+2 x-15=0x2+2x−15=0 . Y = x2 + 2x - 15

Correct AnswerverifiedShow Answer

Factor completely. - x2+20x+100x^{2}+20 x+100x2+20x+100

Correct AnswerverifiedShow Answer

Factor completely. - 4x2−814 x^{2}-814x2−81

Correct AnswerverifiedShow Answer

Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is 768ft2768 \mathrm{ft}^{2}768ft2 , find the length and width of the garden.

Correct AnswerverifiedShow Answer

Factor completely. - 128x2−50128 x^{2}-50128x2−50

Correct AnswerverifiedShow Answer

Solve the problem. -The product of two consecutive integers is 11 more than their sum. Find the integers.

Correct AnswerverifiedShow Answer

Factor. - 6x2+5xt−6t26 x^{2}+5 x t-6 t^{2}6x2+5xt−6t2

Correct AnswerverifiedShow Answer

Solve the problem. -A long-distance runner runs 2 miles south and then 4 miles east. How far is the runner from the starting point? Round to nearest tenth.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Factor. - 6x2−13xy+6y26 x^{2}-13 x y+6 y^{2}6x2−13xy+6y2

Correct AnswerverifiedShow Answer

Factor. - 2x3+6x2−20x2 x^{3}+6 x^{2}-20 x2x3+6x2−20x

Correct AnswerverifiedShow Answer

Factor. - t(8−m) +s(8−m) \mathfrak{t}(8-\mathrm{m}) +\mathrm{s}(8-\mathrm{m}) t(8−m) +s(8−m)

Correct AnswerverifiedShow Answer

Factor. - t2+1.4t+0.49t^{2}+1.4 t+0.49t2+1.4t+0.49

Correct AnswerverifiedShow Answer

Factor completely. - x10+32x5+256x^{10}+32 x^{5}+256x10+32x5+256

Correct AnswerverifiedShow Answer

Factor. - 10z2−7z−1210 z^{2}-7 z-1210z2−7z−12

Correct AnswerverifiedShow Answer

Solve the problem. -The height of a triangle is 4 cm4 \mathrm{~cm}4 cm more than the length of the base. If the area of the triangle is 126 cm2126 \mathrm{~cm}^{2}126 cm2 , find the height and length of the base.

Correct AnswerverifiedShow Answer

Solve the problem. -A number is 12 less than its square. Find all such numbers.

Correct AnswerverifiedShow Answer

Factor. - $4 x^{2}-5 x+9$

Correct Answer
verified

Factor. - $x^{2}+4 x y-21 y^{2}$

Correct Answer
verified

Factor completely. - $4 \mathrm{~m}^{2}-\frac{9}{4}$

Correct Answer
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Solve. -Use the following graph to solve $x^{2}+2 x-15=0$ . Y = x² + 2x - 15 $Solve. -Use the following graph to solve x^{2}+2 x-15=0 . Y = x<sup>2</sup> + 2x - 15 A) -3,5 B) -5,3 C) 3,5 D) -5,-3$

Correct Answer
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Factor completely. - $x^{2}+20 x+100$

Correct Answer
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Factor completely. - $4 x^{2}-81$

Correct Answer
verified

Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is $768 \mathrm{ft}^{2}$ , find the length and width of the garden.

Correct Answer
verified

Factor completely. - $128 x^{2}-50$

Correct Answer
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Correct Answer
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Factor. - $6 x^{2}+5 x t-6 t^{2}$

Correct Answer
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Correct Answer
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Correct Answer
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Factor. - $6 x^{2}-13 x y+6 y^{2}$

Correct Answer
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Factor. - $2 x^{3}+6 x^{2}-20 x$

Correct Answer
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Factor. - $\mathfrak{t}(8-\mathrm{m}) +\mathrm{s}(8-\mathrm{m})$

Correct Answer
verified

Factor. - $t^{2}+1.4 t+0.49$

Correct Answer
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Factor completely. - $x^{10}+32 x^{5}+256$

Correct Answer
verified

Factor. - $10 z^{2}-7 z-12$

Correct Answer
verified

Solve the problem. -The height of a triangle is $4 \mathrm{~cm}$ more than the length of the base. If the area of the triangle is $126 \mathrm{~cm}^{2}$ , find the height and length of the base.

Correct Answer
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Correct Answer
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