Question 1

Factor completely. $6 x ^ { 2 } + 33 x$

Accepted Answer

A)  $3 \left( 2 x ^ { 2 } + 11 x \right)$ 
B)  $2 \left( 3 x ^ { 2 } \right) + 11 ( 3 x )$ 
C)  $2 x ( 3 x ) + 11 ( 3 x )$ 
D)  $x ( 6 x + 33 )$ 
E)  $3 x ( 2 x + 11 )$ 
A)  $3 \left( 2 x ^ { 2 } + 11 x \right)$ 
B)  $2 \left( 3 x ^ { 2 } \right) + 11 ( 3 x )$ 
C)  $2 x ( 3 x ) + 11 ( 3 x )$ 
D)  $x ( 6 x + 33 )$ 
E)  $3 x ( 2 x + 11 )$

Question 2

Factor the expression. $$( x - 4 ) ^ { 2 } + ( x - 4 )$$

Accepted Answer

A)  $( x - 4 ) ( x + 3 )$ 
B)  $( x - 6 ) ( x - 3 )$ 
C)  $( x - 4 ) ( x - 5 )$ 
D)  $( x - 4 ) ( x + 5 )$ 
E)  $( x - 4 ) ( x - 3 )$ 
A)  $( x - 4 ) ( x + 3 )$ 
B)  $( x - 6 ) ( x - 3 )$ 
C)  $( x - 4 ) ( x - 5 )$ 
D)  $( x - 4 ) ( x + 5 )$ 
E)  $( x - 4 ) ( x - 3 )$

Question 3

A rectangle has an area 390 square centimeters. Its length is 4 centimeters more than twice its width. Find the perimeter of the rectangle.

Accepted Answer

A) 78 
B) 98 
C) 94 
D) 86 
A) 78 
B) 98 
C) 94 
D) 86

Question 4

Find the GCF of the numbers below. $12$ , $25$ and $63$

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
A) 1 
B) 2 
C) 3 
D) 4

Question 5

Factor the trinomial, if possible. $$8 a ^ { 2 } + 21 a - 9$$

Accepted Answer

A)  $( 8 a + 3 ) ( a - 3 )$ 
B)  $( 8 a + 3 ) ( a - 4 )$ 
C)  $( 8 a + 3 ) ( a - 5 )$ 
D)  $( 8 a - 3 ) ( a + 3 )$ 
E) prime 
A)  $( 8 a + 3 ) ( a - 3 )$ 
B)  $( 8 a + 3 ) ( a - 4 )$ 
C)  $( 8 a + 3 ) ( a - 5 )$ 
D)  $( 8 a - 3 ) ( a + 3 )$ 
E) prime

Question 6

Factor the polynomial. $$y ^ { 2 } + 18 y + 81$$

Accepted Answer

A)  $( y + 9 ) ^ { 2 }$ 
B)  $( 9 + y ) ( 8 - y )$ 
C)  $( y - 9 ) ( y + 9 )$ 
D)  $( y - 9 ) ^ { 2 }$ 
E) none of these 
A)  $( y + 9 ) ^ { 2 }$ 
B)  $( 9 + y ) ( 8 - y )$ 
C)  $( y - 9 ) ( y + 9 )$ 
D)  $( y - 9 ) ^ { 2 }$ 
E) none of these

Question 7

Factor the expression. $$x ^ { 2 } + 7 x + 3$$

Accepted Answer

A)  $( 3 x + 1 ) ( x + 1 )$ 
B)  $( 2 x + 1 ) ( x + 1 )$ 
C)  $( 2 x + 3 ) ( x - 1 )$ 
D)  $( 2 x - 1 ) ( x + 2 )$ 
E) prime 
A)  $( 3 x + 1 ) ( x + 1 )$ 
B)  $( 2 x + 1 ) ( x + 1 )$ 
C)  $( 2 x + 3 ) ( x - 1 )$ 
D)  $( 2 x - 1 ) ( x + 2 )$ 
E) prime

Question 8

Find the greatest common factor of the numbers below. 111, 123 and 51

Accepted Answer

A) 4 
B) 3 
C) 2 
D) 5 
E) none of these 
A) 4 
B) 3 
C) 2 
D) 5 
E) none of these

Question 9

Solve the equation: $p ( 9 p + 2 ) = 0$

Accepted Answer

A)  $0 , - \frac { 2 } { 9 }$ 
B)  $0 , - 2$ 
C)  $- 1,2$ 
D)  $1 , - \frac { 2 } { 9 }$ 
A)  $0 , - \frac { 2 } { 9 }$ 
B)  $0 , - 2$ 
C)  $- 1,2$ 
D)  $1 , - \frac { 2 } { 9 }$

Question 10

Factor by grouping. $$2 a ^ { 2 } - 3 b c - 2 a b + 3 a c$$

Accepted Answer

A)  $2 a + 3 c ( a - b )$ 
B)  $( 2 a - 3 c ) ( a + b )$ 
C)  $( 2 a + 3 c ) ( a - b )$ 
D)  $( a + c ) ( a - b )$ 
E)  $2 a ^ { 2 } - 2 a b + 3 c ( a - b )$ 
A)  $2 a + 3 c ( a - b )$ 
B)  $( 2 a - 3 c ) ( a + b )$ 
C)  $( 2 a + 3 c ) ( a - b )$ 
D)  $( a + c ) ( a - b )$ 
E)  $2 a ^ { 2 } - 2 a b + 3 c ( a - b )$

Question 11

Factor completely. $$8 x ^ { 2 } - 13 x ^ { 4 } + 12 x ^ { 5 }$$

Accepted Answer

A)  $8 x ^ { 2 } - x ^ { 4 } ( 13 + 12 x )$ 
B)  $x ^ { 2 } \left( 8 - 13 x ^ { 2 } \right) + 12 x ^ { 5 }$ 
C)  $x \left( 8 - 13 x ^ { 3 } + 12 x ^ { 4 } \right)$ 
D)  $x ^ { 2 } \left( 8 + 12 x ^ { 3 } \right) - 13 x ^ { 4 }$ 
E)  $x ^ { 2 } \left( 8 - 13 x ^ { 2 } + 12 x ^ { 3 } \right)$ 
A)  $8 x ^ { 2 } - x ^ { 4 } ( 13 + 12 x )$ 
B)  $x ^ { 2 } \left( 8 - 13 x ^ { 2 } \right) + 12 x ^ { 5 }$ 
C)  $x \left( 8 - 13 x ^ { 3 } + 12 x ^ { 4 } \right)$ 
D)  $x ^ { 2 } \left( 8 + 12 x ^ { 3 } \right) - 13 x ^ { 4 }$ 
E)  $x ^ { 2 } \left( 8 - 13 x ^ { 2 } + 12 x ^ { 3 } \right)$

Question 12

To write a quadratic equation in standard form means that one side of the equation must be zero and the other side must be in the form:

Accepted Answer

A)  $a x + b$ 
B)  $a ^ { 2 } + b x + c$ 
C)  $a x ^ { 2 } + b x + c$ 
D)  $x ^ { 2 } + a c$ 
A)  $a x + b$ 
B)  $a ^ { 2 } + b x + c$ 
C)  $a x ^ { 2 } + b x + c$ 
D)  $x ^ { 2 } + a c$

Question 13

When a wholesaler sells n CD players, the revenue is $R = 150 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 11,250$ ?

Accepted Answer

A)  $120$ CD players 
B)  $190$ CD players 
C)  $150$ CD players 
D)  $130$ CD players 
E)  $140$ CD players 
A)  $120$ CD players 
B)  $190$ CD players 
C)  $150$ CD players 
D)  $130$ CD players 
E)  $140$ CD players

Question 14

Factor the polynomial completely. $64 - 25 y ^ { 2 }$

Accepted Answer

A) (8 + y )(8 + 5 y ) 
B) (8 - 5 y )(8 + 5 y ) 
C) (64 - 5 y )(64 + 5 y ) 
D) (8 - 25 y )(8 + 25 y ) 
E) none of these 
A) (8 + y )(8 + 5 y ) 
B) (8 - 5 y )(8 + 5 y ) 
C) (64 - 5 y )(64 + 5 y ) 
D) (8 - 25 y )(8 + 25 y ) 
E) none of these

Question 15

Solve the equation. $x ^ { 3 } - 11 x ^ { 2 } + 30 x = 0$

Accepted Answer

A) 1, 6 , 5 
B) 0, 6, 5 
C) 6 , 5 
D) -6, -5 
E) 0, -6 , -5 
A) 1, 6 , 5 
B) 0, 6, 5 
C) 6 , 5 
D) -6, -5 
E) 0, -6 , -5

Question 16

Factor the trinomial, if possible. $$12 z ^ { 2 } + 31 z + 20$$

Accepted Answer

A)  $( 3 z + 4 ) ( 5 z - 5 )$ 
B)  $( 3 z + 4 ) ( 2 z + 5 )$ 
C)  $( 3 z + 4 ) ( 4 z + 5 )$ 
D)  $( 3 z + 4 ) ( 3 z - 5 )$ 
E) prime 
A)  $( 3 z + 4 ) ( 5 z - 5 )$ 
B)  $( 3 z + 4 ) ( 2 z + 5 )$ 
C)  $( 3 z + 4 ) ( 4 z + 5 )$ 
D)  $( 3 z + 4 ) ( 3 z - 5 )$ 
E) prime

Question 17

Factor the expression. $$y ^ { 2 } - 4 y + 4$$

Accepted Answer

A)  $( y + 2 ) ( y + 2 )$ 
B)  $( y - 2 ) ( y + 2 )$ 
C)  $( y + 4 ) ( y + 1 )$ 
D)  $( y - 2 ) ( y - 2 )$ 
E) prime 
A)  $( y + 2 ) ( y + 2 )$ 
B)  $( y - 2 ) ( y + 2 )$ 
C)  $( y + 4 ) ( y + 1 )$ 
D)  $( y - 2 ) ( y - 2 )$ 
E) prime

Question 18

Factor the expression. Factor out any greatest common factors first. $$4 x ^ { 3 } + 32$$

Accepted Answer

A)  $4 ( x - 2 ) \left( x ^ { 2 } + 8 x + 4 \right)$ 
B)  $4 ( x + 4 ) \left( x ^ { 2 } + 4 x + 4 \right)$ 
C)  $2 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$ 
D)  $4 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
E)  $2 ( x + 4 ) \left( x ^ { 2 } + 4 x - 16 \right)$ 
A)  $4 ( x - 2 ) \left( x ^ { 2 } + 8 x + 4 \right)$ 
B)  $4 ( x + 4 ) \left( x ^ { 2 } + 4 x + 4 \right)$ 
C)  $2 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$ 
D)  $4 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
E)  $2 ( x + 4 ) \left( x ^ { 2 } + 4 x - 16 \right)$

Question 19

The inclined ramp of the boat launch shown in the illustration is 10 meters longer than the "rise" of the ramp. The "run" is 5 meters longer than the "rise". How long is the "rise" of the ramp?

Accepted Answer

A) 25 m 
B) 7.5 m 
C) 20 m 
D) 15 m 
E) 14 m 
A) 25 m 
B) 7.5 m 
C) 20 m 
D) 15 m 
E) 14 m

Question 20

Factor the following perfect square trinomial. $$49 x ^ { 2 } + 14 x + 1$$

Accepted Answer

A)  $( 7 x + 14 ) ^ { 2 }$ 
B)  $( x + 7 ) ^ { 2 }$ 
C)  $( 7 x - 1 ) ^ { 2 }$ 
D)  $( x - 7 ) ^ { 2 }$ 
E)  $( 7 x + 1 ) ^ { 2 }$ 
A)  $( 7 x + 14 ) ^ { 2 }$ 
B)  $( x + 7 ) ^ { 2 }$ 
C)  $( 7 x - 1 ) ^ { 2 }$ 
D)  $( x - 7 ) ^ { 2 }$ 
E)  $( 7 x + 1 ) ^ { 2 }$

Factor completely. $6 x ^ { 2 } + 33 x$

Factor the expression. $( x - 4 ) ^ { 2 } + ( x - 4 )$

A rectangle has an area 390 square centimeters. Its length is 4 centimeters more than twice its width. Find the perimeter of the rectangle.

Find the GCF of the numbers below. $12$ , $25$ and $63$

Factor the trinomial, if possible. $8 a ^ { 2 } + 21 a - 9$

Factor the polynomial. $y ^ { 2 } + 18 y + 81$

Factor the expression. $x ^ { 2 } + 7 x + 3$

Find the greatest common factor of the numbers below. 111, 123 and 51

Solve the equation: $p ( 9 p + 2 ) = 0$

Factor by grouping. $2 a ^ { 2 } - 3 b c - 2 a b + 3 a c$

Factor completely. $8 x ^ { 2 } - 13 x ^ { 4 } + 12 x ^ { 5 }$

To write a quadratic equation in standard form means that one side of the equation must be zero and the other side must be in the form:

When a wholesaler sells n CD players, the revenue is $R = 150 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 11,250$ ?

Factor the polynomial completely. $64 - 25 y ^ { 2 }$

Solve the equation. $x ^ { 3 } - 11 x ^ { 2 } + 30 x = 0$

Factor the trinomial, if possible. $12 z ^ { 2 } + 31 z + 20$

Factor the expression. $y ^ { 2 } - 4 y + 4$

Factor the expression. Factor out any greatest common factors first. $4 x ^ { 3 } + 32$

The inclined ramp of the boat launch shown in the illustration is 10 meters longer than the "rise" of the ramp. The "run" is 5 meters longer than the "rise". How long is the "rise" of the ramp?

Factor the following perfect square trinomial. $49 x ^ { 2 } + 14 x + 1$

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 6: Factoring and Quadratic Equations

Factor completely. 6x2+33x6 x ^ { 2 } + 33 x6x2+33x

Factor the expression. (x−4)2+(x−4)( x - 4 ) ^ { 2 } + ( x - 4 )(x−4)2+(x−4)

A rectangle has an area 390 square centimeters. Its length is 4 centimeters more than twice its width. Find the perimeter of the rectangle.

Find the GCF of the numbers below. 121212 , 252525 and 636363

Factor the trinomial, if possible. 8a2+21a−98 a ^ { 2 } + 21 a - 98a2+21a−9

Factor the polynomial. y2+18y+81y ^ { 2 } + 18 y + 81y2+18y+81

Factor the expression. x2+7x+3x ^ { 2 } + 7 x + 3x2+7x+3

Find the greatest common factor of the numbers below. 111, 123 and 51

Solve the equation: p(9p+2)=0p ( 9 p + 2 ) = 0p(9p+2)=0

Factor by grouping. 2a2−3bc−2ab+3ac2 a ^ { 2 } - 3 b c - 2 a b + 3 a c2a2−3bc−2ab+3ac

Factor completely. 8x2−13x4+12x58 x ^ { 2 } - 13 x ^ { 4 } + 12 x ^ { 5 }8x2−13x4+12x5

To write a quadratic equation in standard form means that one side of the equation must be zero and the other side must be in the form:

When a wholesaler sells n CD players, the revenue is R=150n−12n2R = 150 n - \frac { 1 } { 2 } n ^ { 2 }R=150n−21​n2 . How many CD players would the wholesaler have to sell to receive $11,250\$ 11,250$11,250 ?

Factor the polynomial completely. 64−25y264 - 25 y ^ { 2 }64−25y2

Solve the equation. x3−11x2+30x=0x ^ { 3 } - 11 x ^ { 2 } + 30 x = 0x3−11x2+30x=0

Factor the trinomial, if possible. 12z2+31z+2012 z ^ { 2 } + 31 z + 2012z2+31z+20

Factor the expression. y2−4y+4y ^ { 2 } - 4 y + 4y2−4y+4

Factor the expression. Factor out any greatest common factors first. 4x3+324 x ^ { 3 } + 324x3+32

The inclined ramp of the boat launch shown in the illustration is 10 meters longer than the "rise" of the ramp. The "run" is 5 meters longer than the "rise". How long is the "rise" of the ramp?

Factor the following perfect square trinomial. 49x2+14x+149 x ^ { 2 } + 14 x + 149x2+14x+1

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Factor completely. $6 x ^ { 2 } + 33 x$

Factor the expression. $( x - 4 ) ^ { 2 } + ( x - 4 )$

Find the GCF of the numbers below. $12$ , $25$ and $63$

Factor the trinomial, if possible. $8 a ^ { 2 } + 21 a - 9$

Factor the polynomial. $y ^ { 2 } + 18 y + 81$

Factor the expression. $x ^ { 2 } + 7 x + 3$

Solve the equation: $p ( 9 p + 2 ) = 0$

Factor by grouping. $2 a ^ { 2 } - 3 b c - 2 a b + 3 a c$

Factor completely. $8 x ^ { 2 } - 13 x ^ { 4 } + 12 x ^ { 5 }$

When a wholesaler sells n CD players, the revenue is $R = 150 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 11,250$ ?

Factor the polynomial completely. $64 - 25 y ^ { 2 }$

Solve the equation. $x ^ { 3 } - 11 x ^ { 2 } + 30 x = 0$

Factor the trinomial, if possible. $12 z ^ { 2 } + 31 z + 20$

Factor the expression. $y ^ { 2 } - 4 y + 4$

Factor the expression. Factor out any greatest common factors first. $4 x ^ { 3 } + 32$

Factor the following perfect square trinomial. $49 x ^ { 2 } + 14 x + 1$