Question 1

Use the rational root theorem and the factor theorem to help solve the equation. x  3 - x  2 - 65 x + 225 = 0

Accepted Answer

A) {-9, 5} 
B) {-5, 9} 
C) {-8 , 3} 
D) {-9, 3} 
E) {-8, 5} 
A) {-9, 5} 
B) {-5, 9} 
C) {-8 , 3} 
D) {-9, 3} 
E) {-8, 5}

Question 2

Simplify the expression. $$( 5 x + 5 ) + ( 9 x - 3 )$$

Accepted Answer

A)  $14 x + 2$ 
B)  $14 x - 2$ 
C)  $14 x + 5$ 
D)  $5 x + 2$ 
E) none of these 
A)  $14 x + 2$ 
B)  $14 x - 2$ 
C)  $14 x + 5$ 
D)  $5 x + 2$ 
E) none of these

Question 3

The length of an altitude of a triangle is $\frac { 1 } { 2 }$ the length of the side to which it is drawn. If the area of the triangle is 75 square centimeters, find the length of that altitude.

Accepted Answer

A) 5 centimeters 
B) 4 centimeters 
C) 10 centimeters 
D) 3 centimeters 
E) 8 centimeters 
A) 5 centimeters 
B) 4 centimeters 
C) 10 centimeters 
D) 3 centimeters 
E) 8 centimeters

Question 4

Determine the degree of the given polynomial. -5

Accepted Answer

A) 0 
B) 9 
C) 5 
D) 7 
E) 4 
A) 0 
B) 9 
C) 5 
D) 7 
E) 4

Question 5

Determine the degree of the given polynomial. $$3 x ^ { 3 } y ^ { 2 } - 9 x ^ { 3 } y ^ { 3 }$$

Accepted Answer

A) 5 
B) 0 
C) 3 
D) 6 
E) 1 
A) 5 
B) 0 
C) 3 
D) 6 
E) 1

Question 6

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

Accepted Answer

A)  $( c - 7 ) ^ { 2 }$ 
B)  $( c + 6 ) ^ { 2 }$ 
C)  $( c + 14 ) ^ { 2 }$ 
D)  $( c + 7 ) ^ { 2 }$ 
E) none of these 
A)  $( c - 7 ) ^ { 2 }$ 
B)  $( c + 6 ) ^ { 2 }$ 
C)  $( c + 14 ) ^ { 2 }$ 
D)  $( c + 7 ) ^ { 2 }$ 
E) none of these

Question 7

The combined area of two squares is 153 square meters. The sides of the larger square are 4 times as long as the sides of the smaller square. Find the dimensions of each of the squares.

Accepted Answer

A) Dimensions of the smaller square are 4 by 4 meters, dimensions of the larger square are 16 by 16 meters. 
B) Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 4 by 4 meters. 
C) Dimensions of the smaller square are 8 by 8 meters, dimensions of the larger square are 32 by 32 meters. 
D) Dimensions of the smaller square are 3 by 3 meters, dimensions of the larger square are 12 by 12 meters. 
E) Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 8 by 8 meters. 
A) Dimensions of the smaller square are 4 by 4 meters, dimensions of the larger square are 16 by 16 meters. 
B) Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 4 by 4 meters. 
C) Dimensions of the smaller square are 8 by 8 meters, dimensions of the larger square are 32 by 32 meters. 
D) Dimensions of the smaller square are 3 by 3 meters, dimensions of the larger square are 12 by 12 meters. 
E) Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 8 by 8 meters.

Question 8

Find the product. $$6 t ^ { 2 } \left( 6 t ^ { 2 } - 2 t - 10 \right)$$

Accepted Answer

The answer of Find the product. \[6 t ^ {...

Question 9

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 16$

Accepted Answer

A) ( x - 4)( x + 4) 
B) ( x + 4)( x + 16) 
C) ( x - 4)( x - 16) 
D) ( x - 16)( x + 16) 
E) none of these 
A) ( x - 4)( x + 4) 
B) ( x + 4)( x + 16) 
C) ( x - 4)( x - 16) 
D) ( x - 16)( x + 16) 
E) none of these

Question 10

Solve the equation. $x ^ { 3 } + 7 x ^ { 2 } = x ^ { 2 } - 9 x$

Accepted Answer

A)  $x = 3,0$ 
B)  $x = - 3$ 
C)  $x = - 3,0$ 
D)  $x = - 3,3,0$ 
E)  $x = 3$ 
A)  $x = 3,0$ 
B)  $x = - 3$ 
C)  $x = - 3,0$ 
D)  $x = - 3,3,0$ 
E)  $x = 3$

Question 11

Find the indicated product. ( x + 3) 3

Accepted Answer

A) x  3 + 9 x  2 + 27 x + 27 
B) x  3 + 27 x  2 + 9 x + 27 
C) x  3 + 3 x  2 + 9 x + 27 
D) x  3 + 9 x  2 + 9 x + 3 
E) x  3 + 9 x  2 + 27 x + 9 
A) x  3 + 9 x  2 + 27 x + 27 
B) x  3 + 27 x  2 + 9 x + 27 
C) x  3 + 3 x  2 + 9 x + 27 
D) x  3 + 9 x  2 + 9 x + 3 
E) x  3 + 9 x  2 + 27 x + 9

Question 12

Factor completely. $$5 x ( 9 a + b ) - 17 y ( 9 a + b )$$

Accepted Answer

A)  $( 5 x - 17 y ) ( 9 a + b )$ 
B)  $45 a x - 153 a y - 5 b x + 34 b y$ 
C)  $5 x - 17 y ( 9 a + b )$ 
D)  $( 5 x - 17 y ) 9 a + b$ 
E)  $45 a x - 153 a y + 5 b x - 17 b y$ 
A)  $( 5 x - 17 y ) ( 9 a + b )$ 
B)  $45 a x - 153 a y - 5 b x + 34 b y$ 
C)  $5 x - 17 y ( 9 a + b )$ 
D)  $( 5 x - 17 y ) 9 a + b$ 
E)  $45 a x - 153 a y + 5 b x - 17 b y$

Question 13

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } + 12 x = 0$

Accepted Answer

A) 1, 4 , 3 
B) 0, 4, 3 
C) 4 , 3 
D) -4, -3 
E) 0, -4 , -3 
A) 1, 4 , 3 
B) 0, 4, 3 
C) 4 , 3 
D) -4, -3 
E) 0, -4 , -3

Question 14

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor the following. 1 - 27 a 3

Accepted Answer

A) ( 1 - 3 a )( 1 - 6 a + 9 a 2 ) 
B) ( 1 - 3 a )( 1 - 3 a + 9 a 2 ) 
C) ( 1 - 3 a )( 1 + 3 a + 9 a 2 ) 
D) ( 1 + 3 a )( 1 + 3 a + 9 a 2 ) 
E) ( 1 - 3 a )( 1 + 6 a + 9 a 2 ) 
A) ( 1 - 3 a )( 1 - 6 a + 9 a 2 ) 
B) ( 1 - 3 a )( 1 - 3 a + 9 a 2 ) 
C) ( 1 - 3 a )( 1 + 3 a + 9 a 2 ) 
D) ( 1 + 3 a )( 1 + 3 a + 9 a 2 ) 
E) ( 1 - 3 a )( 1 + 6 a + 9 a 2 )

Question 15

Use the rational root theorem and the factor theorem to help solve the equation. x  3 - 3 x  2 + x - 3 = 0

Accepted Answer

A)  $\{ 3 , \pm i \}$ 
B)  $\{ 3,3 , \pm i \}$ 
C)  $\{ 2 , \pm i \}$ 
D)  $\{ 2,3 , \pm i \}$ 
E)  $\{ 4 , \pm 2 i \}$ 
A)  $\{ 3 , \pm i \}$ 
B)  $\{ 3,3 , \pm i \}$ 
C)  $\{ 2 , \pm i \}$ 
D)  $\{ 2,3 , \pm i \}$ 
E)  $\{ 4 , \pm 2 i \}$

Question 16

Suppose that the length of a rectangle is 9 and one-third times as long as its width. The area of the rectangle is 1,344 square centimeters. Find the length and width of the rectangle.

Accepted Answer

A) The width of the rectangle is 12 and the length of the rectangle is 112. 
B) The width of the rectangle is 17 and the length of the rectangle is 122. 
C) The width of the rectangle is 11 and the length of the rectangle is 28. 
D) The width of the rectangle is 14 and the length of the rectangle is 117. 
E) The width of the rectangle is 10 and the length of the rectangle is 112. 
A) The width of the rectangle is 12 and the length of the rectangle is 112. 
B) The width of the rectangle is 17 and the length of the rectangle is 122. 
C) The width of the rectangle is 11 and the length of the rectangle is 28. 
D) The width of the rectangle is 14 and the length of the rectangle is 117. 
E) The width of the rectangle is 10 and the length of the rectangle is 112.

Question 17

Classify the number as prime or composite. 19

Accepted Answer

A) Prime 
B) Composite 
A) Prime 
B) Composite

Question 18

Factor the expression. $$- 20 a b c - 20 a c ^ { 2 } + 4 b c + 4 c ^ { 2 }$$

Accepted Answer

A)  $- 4 c ( b - c ) ( 5 a + 1 )$ 
B)  $- 4 c ( b - 1 ) ( 5 a + c )$ 
C)  $- 4 c ( b + c ) ( 5 a - 1 )$ 
D)  $4 c ( b - 1 ) ( 5 a + c )$ 
E)  $- 4 c ( b + 1 ) ( 5 a - c )$ 
A)  $- 4 c ( b - c ) ( 5 a + 1 )$ 
B)  $- 4 c ( b - 1 ) ( 5 a + c )$ 
C)  $- 4 c ( b + c ) ( 5 a - 1 )$ 
D)  $4 c ( b - 1 ) ( 5 a + c )$ 
E)  $- 4 c ( b + 1 ) ( 5 a - c )$

Question 19

The combined area of a square and a rectangle is 102 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 4 centimeters more than its width. Find the dimensions of the square and the rectangle.

Accepted Answer

A) 5 centimeters by 7 centimeters and 11 centimeters by 11 centimeters 
B) 7 centimeters by 7 centimeters and 5 centimeters by 9 centimeters 
C) 5 centimeters by 5 centimeters and 7 centimeters by 11 centimeters 
D) 5 centimeters by 5 centimeters and 7 centimeters by 9 centimeters 
E) none of these 
A) 5 centimeters by 7 centimeters and 11 centimeters by 11 centimeters 
B) 7 centimeters by 7 centimeters and 5 centimeters by 9 centimeters 
C) 5 centimeters by 5 centimeters and 7 centimeters by 11 centimeters 
D) 5 centimeters by 5 centimeters and 7 centimeters by 9 centimeters 
E) none of these

Question 20

Factor the composite number $66$ into the product of prime numbers. For example: 30 = 2 * 3 * 5.

Accepted Answer

A)  $1 \cdot 3 \cdot 11$ 
B)  $2 \cdot 33$ 
C)  $1 \cdot 6 \cdot 11$ 
D)  $2 \cdot 3 \cdot 11$ 
E)  $3 \cdot 1.22$ 
A)  $1 \cdot 3 \cdot 11$ 
B)  $2 \cdot 33$ 
C)  $1 \cdot 6 \cdot 11$ 
D)  $2 \cdot 3 \cdot 11$ 
E)  $3 \cdot 1.22$

Use the rational root theorem and the factor theorem to help solve the equation. x ³ - x ² - 65 x + 225 = 0

Simplify the expression. $( 5 x + 5 ) + ( 9 x - 3 )$

The length of an altitude of a triangle is $\frac { 1 } { 2 }$ the length of the side to which it is drawn. If the area of the triangle is 75 square centimeters, find the length of that altitude.

Determine the degree of the given polynomial. -5

Determine the degree of the given polynomial. $3 x ^ { 3 } y ^ { 2 } - 9 x ^ { 3 } y ^ { 3 }$

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

The combined area of two squares is 153 square meters. The sides of the larger square are 4 times as long as the sides of the smaller square. Find the dimensions of each of the squares.

Find the product. $6 t ^ { 2 } \left( 6 t ^ { 2 } - 2 t - 10 \right)$

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 16$

Solve the equation. $x ^ { 3 } + 7 x ^ { 2 } = x ^ { 2 } - 9 x$

Find the indicated product. ( x + 3)³

Factor completely. $5 x ( 9 a + b ) - 17 y ( 9 a + b )$

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } + 12 x = 0$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor the following. 1 - 27 a³

Use the rational root theorem and the factor theorem to help solve the equation. x ³ - 3 x ² + x - 3 = 0

Suppose that the length of a rectangle is 9 and one-third times as long as its width. The area of the rectangle is 1,344 square centimeters. Find the length and width of the rectangle.

Classify the number as prime or composite. 19

Factor the expression. $- 20 a b c - 20 a c ^ { 2 } + 4 b c + 4 c ^ { 2 }$

The combined area of a square and a rectangle is 102 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 4 centimeters more than its width. Find the dimensions of the square and the rectangle.

Factor the composite number $66$ into the product of prime numbers. For example: 30 = 2 * 3 * 5.

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 3: Polynomials

Use the rational root theorem and the factor theorem to help solve the equation. x 3 - x 2 - 65 x + 225 = 0

Simplify the expression. (5x+5)+(9x−3)( 5 x + 5 ) + ( 9 x - 3 )(5x+5)+(9x−3)

The length of an altitude of a triangle is 12\frac { 1 } { 2 }21​ the length of the side to which it is drawn. If the area of the triangle is 75 square centimeters, find the length of that altitude.

Determine the degree of the given polynomial. -5

Determine the degree of the given polynomial. 3x3y2−9x3y33 x ^ { 3 } y ^ { 2 } - 9 x ^ { 3 } y ^ { 3 }3x3y2−9x3y3

Factor the following perfect square trinomial. c2+14c+49c ^ { 2 } + 14 c + 49c2+14c+49

The combined area of two squares is 153 square meters. The sides of the larger square are 4 times as long as the sides of the smaller square. Find the dimensions of each of the squares.

Find the product. 6t2(6t2−2t−10)6 t ^ { 2 } \left( 6 t ^ { 2 } - 2 t - 10 \right)6t2(6t2−2t−10)

Use the difference of squares pattern to factor the polynomial. x2−16x ^ { 2 } - 16x2−16

Solve the equation. x3+7x2=x2−9xx ^ { 3 } + 7 x ^ { 2 } = x ^ { 2 } - 9 xx3+7x2=x2−9x

Find the indicated product. ( x + 3) 3

Factor completely. 5x(9a+b)−17y(9a+b)5 x ( 9 a + b ) - 17 y ( 9 a + b )5x(9a+b)−17y(9a+b)

Solve the equation. x3−7x2+12x=0x ^ { 3 } - 7 x ^ { 2 } + 12 x = 0x3−7x2+12x=0

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor the following. 1 - 27 a 3

Use the rational root theorem and the factor theorem to help solve the equation. x 3 - 3 x 2 + x - 3 = 0

Suppose that the length of a rectangle is 9 and one-third times as long as its width. The area of the rectangle is 1,344 square centimeters. Find the length and width of the rectangle.

Classify the number as prime or composite. 19

Factor the expression. −20abc−20ac2+4bc+4c2- 20 a b c - 20 a c ^ { 2 } + 4 b c + 4 c ^ { 2 }−20abc−20ac2+4bc+4c2

The combined area of a square and a rectangle is 102 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 4 centimeters more than its width. Find the dimensions of the square and the rectangle.

Factor the composite number 666666 into the product of prime numbers. For example: 30 = 2 * 3 * 5.

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Use the rational root theorem and the factor theorem to help solve the equation. x ³ - x ² - 65 x + 225 = 0

Simplify the expression. $( 5 x + 5 ) + ( 9 x - 3 )$

The length of an altitude of a triangle is $\frac { 1 } { 2 }$ the length of the side to which it is drawn. If the area of the triangle is 75 square centimeters, find the length of that altitude.

Determine the degree of the given polynomial. $3 x ^ { 3 } y ^ { 2 } - 9 x ^ { 3 } y ^ { 3 }$

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

Find the product. $6 t ^ { 2 } \left( 6 t ^ { 2 } - 2 t - 10 \right)$

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 16$

Solve the equation. $x ^ { 3 } + 7 x ^ { 2 } = x ^ { 2 } - 9 x$

Find the indicated product. ( x + 3)³

Factor completely. $5 x ( 9 a + b ) - 17 y ( 9 a + b )$

Solve the equation. $x ^ { 3 } - 7 x ^ { 2 } + 12 x = 0$

Use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor the following. 1 - 27 a³

Use the rational root theorem and the factor theorem to help solve the equation. x ³ - 3 x ² + x - 3 = 0

Factor the expression. $- 20 a b c - 20 a c ^ { 2 } + 4 b c + 4 c ^ { 2 }$

Factor the composite number $66$ into the product of prime numbers. For example: 30 = 2 * 3 * 5.