Question 1

Factor the polynomial completely. $4 a ^ { 4 } + 25 a ^ { 2 }$

Accepted Answer

A)  $a ^ { 2 } \left( 4 a ^ { 2 } + 25 \right)$ 
B)  $a ^ { 2 } \left( 4 a ^ { 2 } - 25 \right)$ 
C)  $a \left( 4 a ^ { 3 } + 25 a \right)$ 
D)  $a ^ { 2 } ( 2 a + 5 ) ( 2 a - 5 )$ 
E)  none of these 
A)  $a ^ { 2 } \left( 4 a ^ { 2 } + 25 \right)$ 
B)  $a ^ { 2 } \left( 4 a ^ { 2 } - 25 \right)$ 
C)  $a \left( 4 a ^ { 3 } + 25 a \right)$ 
D)  $a ^ { 2 } ( 2 a + 5 ) ( 2 a - 5 )$ 
E)  none of these

Question 2

Solve the equation. $x ^ { 2 } + 25 x + 154$ = 0 Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(x ^ { 2...

Question 3

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 10 x ^ { a } + 21$

Accepted Answer

A)  $\left( x ^ { a } - 7 \right) \left( x ^ { a } + 3 \right)$ 
B)  $\left( x ^ { a } + 7 \right) \left( x ^ { a } - 3 \right)$ 
C)  $\left( x ^ { a } + 7 \right) \left( x ^ { a } + 3 \right)$ 
D)  $\left( x ^ { a } - 7 \right) \left( x ^ { a } - 3 \right)$ 
A)  $\left( x ^ { a } - 7 \right) \left( x ^ { a } + 3 \right)$ 
B)  $\left( x ^ { a } + 7 \right) \left( x ^ { a } - 3 \right)$ 
C)  $\left( x ^ { a } + 7 \right) \left( x ^ { a } + 3 \right)$ 
D)  $\left( x ^ { a } - 7 \right) \left( x ^ { a } - 3 \right)$

Question 4

Solve the equation. $- x ^ { 2 } - 6 x + 7 = 0$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(- x ^ {...

Question 5

Solve the equation. $20 x ^ { 2 } + 43 x = - 14$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 4 } , - \frac { 2 } { 5 } \right\}$ 
B)  $\left\{ \frac { 7 } { 4 } , \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 7 } { 4 } , \frac { 5 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 4 } , \frac { 2 } { 5 } \right\}$ 
E)  $\left\{ \frac { 7 } { 4 } , - \frac { 2 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 4 } , - \frac { 2 } { 5 } \right\}$ 
B)  $\left\{ \frac { 7 } { 4 } , \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 7 } { 4 } , \frac { 5 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 4 } , \frac { 2 } { 5 } \right\}$ 
E)  $\left\{ \frac { 7 } { 4 } , - \frac { 2 } { 5 } \right\}$

Question 6

Factor this trinomial completely. $10 x ^ { 2 } - 11 x y - 6 y ^ { 2 }$

Accepted Answer

A)  (10 x + 3 y ) ( x $-$ 2 y ) 
B)  (2 x + 3 y )(5 x $-$ 2 y ) 
C)  (2 x $-$ 3 y )(5 x + 4 y ) 
D)  (2 x $-$ 3 y )(5 x + 2 y ) 
E)  not factorable 
A)  (10 x + 3 y ) ( x $-$ 2 y ) 
B)  (2 x + 3 y )(5 x $-$ 2 y ) 
C)  (2 x $-$ 3 y )(5 x + 4 y ) 
D)  (2 x $-$ 3 y )(5 x + 2 y ) 
E)  not factorable

Question 7

Solve the equation. $( u - 8 ) ( u + 2 ) = - 24$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(( u - 8...

Question 8

Factor the trinomial completely. Indicate if it is not factorable using integers. $14 x ^ { 2 } - 52 x + 30$

Accepted Answer

A)  $( 7 x - 5 ) ( x - 3 )$ 
B)  $( 7 x + 5 ) ( x - 3 )$ 
C)  $2 ( 7 x - 5 ) ( x - 3 )$ 
D)  $2 ( 7 x - 5 ) ( x + 3 )$ 
E)  not factorable 
A)  $( 7 x - 5 ) ( x - 3 )$ 
B)  $( 7 x + 5 ) ( x - 3 )$ 
C)  $2 ( 7 x - 5 ) ( x - 3 )$ 
D)  $2 ( 7 x - 5 ) ( x + 3 )$ 
E)  not factorable

Question 9

The area of a triangle is 14 square inches. One side of the triangle is 17 inches less than three times the length of the altitude to that side. Find the length of that side.

Accepted Answer

A)  3 in. 
B)  4 in. 
C)  2 in. 
D)  5 in. 
E)  6 in. 
A)  3 in. 
B)  4 in. 
C)  2 in. 
D)  5 in. 
E)  6 in.

Question 10

Factor the following perfect square trinomial. $b ^ { 2 } + 4 b + 4$

Accepted Answer

A)  $( b + 2 ) ^ { 2 }$ 
B)  $( b - 2 ) ^ { 2 }$ 
C)  $( b + 4 ) ^ { 2 }$ 
D)  none of these 
A)  $( b + 2 ) ^ { 2 }$ 
B)  $( b - 2 ) ^ { 2 }$ 
C)  $( b + 4 ) ^ { 2 }$ 
D)  none of these

Question 11

Set up an equation and solve the problem. The sum of the areas of two squares is 4,477 square inches. Each side of the larger square is 6 times the length of a side of the smaller square. Find the length of a side of the smaller square. __________ inches

Accepted Answer

The answer of Set up an equation and solve the...

Question 12

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 49$

Accepted Answer

A)  ( x $-$ 7) ( x + 7) 
B)  ( x $-$ 49) ( x + 49) 
C)  ( x + 7) ( x + 49) 
D)  ( x $-$ 7) ( x $-$ 49) 
E)  none of these 
A)  ( x $-$ 7) ( x + 7) 
B)  ( x $-$ 49) ( x + 49) 
C)  ( x + 7) ( x + 49) 
D)  ( x $-$ 7) ( x $-$ 49) 
E)  none of these

Question 13

Factor the following trinomial completely. $x ^ { 2 } + 16 x + 63$

Accepted Answer

A)  ( x $-$ 9)( x + 7) 
B)  x ( x + 16) + 63 
C)  ( x + 9)( x + 7) 
D)  ( x + 9)( x $-$ 7) 
E)  ( x $-$ 9)( x $-$ 7) 
A)  ( x $-$ 9)( x + 7) 
B)  x ( x + 16) + 63 
C)  ( x + 9)( x + 7) 
D)  ( x + 9)( x $-$ 7) 
E)  ( x $-$ 9)( x $-$ 7)

Question 14

Solve the equation. $( p - 8 ) ( p + 1 ) = - 20$

Accepted Answer

A)  {8, -1} 
B)  {8, 0} 
C)  {7, 3} 
D)  {4, 3} 
E)  none of these 
A)  {8, -1} 
B)  {8, 0} 
C)  {7, 3} 
D)  {4, 3} 
E)  none of these

Question 15

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

Accepted Answer

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

Question 16

An apple orchard contains 66 trees. The number of trees per row is five more than the number of rows. Find the number of rows.

Accepted Answer

A)  9 
B)  11 
C)  3 
D)  6 
A)  9 
B)  11 
C)  3 
D)  6

Question 17

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 10 z - 5$

Accepted Answer

A)  $( 2 z - 1 ) ( z + 5 )$ 
B)  $( 2 z + 1 ) ( z - 5 )$ 
C)  $( 2 z + 10 ) ( z - 5 )$ 
D)  $( 2 z - 10 ) ( z - 1 )$ 
E)  $( 2 z - 10 ) ( z + 1 )$ 
A)  $( 2 z - 1 ) ( z + 5 )$ 
B)  $( 2 z + 1 ) ( z - 5 )$ 
C)  $( 2 z + 10 ) ( z - 5 )$ 
D)  $( 2 z - 10 ) ( z - 1 )$ 
E)  $( 2 z - 10 ) ( z + 1 )$

Question 18

Factor the following perfect square trinomial. $64 a ^ { 2 } - 48 a n + 9 n ^ { 2 }$

Accepted Answer

The answer of Factor the following perfect square trinomial. \(64...

Question 19

Factor the following polynomial completely. $3 a ^ { 4 } - 243$

Accepted Answer

A)  $3 ( a + 3 ) \left( a ^ { 2 } + 9 \right)$ 
B)  $3 \left( a ^ { 2 } - 9 \right) \left( a ^ { 2 } + 9 \right)$ 
C)  $3 ( a - 3 ) ( a + 3 ) \left( a ^ { 2 } + 9 \right)$ 
D)  $( a - 3 ) ( a + 3 ) \left( a ^ { 2 } + 9 \right)$ 
E)  none of these 
A)  $3 ( a + 3 ) \left( a ^ { 2 } + 9 \right)$ 
B)  $3 \left( a ^ { 2 } - 9 \right) \left( a ^ { 2 } + 9 \right)$ 
C)  $3 ( a - 3 ) ( a + 3 ) \left( a ^ { 2 } + 9 \right)$ 
D)  $( a - 3 ) ( a + 3 ) \left( a ^ { 2 } + 9 \right)$ 
E)  none of these

Question 20

Solve the equation. $3 x ^ { 2 } = 867$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(3 x ^ {...

Factor the polynomial completely. $4 a ^ { 4 } + 25 a ^ { 2 }$

Solve the equation. $x ^ { 2 } + 25 x + 154$ = 0 Please enter your answer as two numbers, separated by a comma.

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 10 x ^ { a } + 21$

Solve the equation. $- x ^ { 2 } - 6 x + 7 = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $20 x ^ { 2 } + 43 x = - 14$

Factor this trinomial completely. $10 x ^ { 2 } - 11 x y - 6 y ^ { 2 }$

Solve the equation. $( u - 8 ) ( u + 2 ) = - 24$ Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. $14 x ^ { 2 } - 52 x + 30$

The area of a triangle is 14 square inches. One side of the triangle is 17 inches less than three times the length of the altitude to that side. Find the length of that side.

Factor the following perfect square trinomial. $b ^ { 2 } + 4 b + 4$

Set up an equation and solve the problem. The sum of the areas of two squares is 4,477 square inches. Each side of the larger square is 6 times the length of a side of the smaller square. Find the length of a side of the smaller square. __________ inches

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 49$

Factor the following trinomial completely. $x ^ { 2 } + 16 x + 63$

Solve the equation. $( p - 8 ) ( p + 1 ) = - 20$

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

An apple orchard contains 66 trees. The number of trees per row is five more than the number of rows. Find the number of rows.

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 10 z - 5$

Factor the following perfect square trinomial. $64 a ^ { 2 } - 48 a n + 9 n ^ { 2 }$

Factor the following polynomial completely. $3 a ^ { 4 } - 243$

Solve the equation. $3 x ^ { 2 } = 867$ Please enter your answer as two numbers, separated by a comma.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 7: Factoring, Solving Equations and Problem Solving

Factor the polynomial completely. 4a4+25a24 a ^ { 4 } + 25 a ^ { 2 }4a4+25a2

Solve the equation. x2+25x+154x ^ { 2 } + 25 x + 154x2+25x+154 = 0 Please enter your answer as two numbers, separated by a comma.

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. x2a+10xa+21x ^ { 2 a } + 10 x ^ { a } + 21x2a+10xa+21

Solve the equation. −x2−6x+7=0- x ^ { 2 } - 6 x + 7 = 0−x2−6x+7=0 Please enter your answer as two numbers, separated by a comma.

Solve the equation. 20x2+43x=−1420 x ^ { 2 } + 43 x = - 1420x2+43x=−14

Factor this trinomial completely. 10x2−11xy−6y210 x ^ { 2 } - 11 x y - 6 y ^ { 2 }10x2−11xy−6y2

Solve the equation. (u−8)(u+2)=−24( u - 8 ) ( u + 2 ) = - 24(u−8)(u+2)=−24 Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. 14x2−52x+3014 x ^ { 2 } - 52 x + 3014x2−52x+30

The area of a triangle is 14 square inches. One side of the triangle is 17 inches less than three times the length of the altitude to that side. Find the length of that side.

Factor the following perfect square trinomial. b2+4b+4b ^ { 2 } + 4 b + 4b2+4b+4

Set up an equation and solve the problem. The sum of the areas of two squares is 4,477 square inches. Each side of the larger square is 6 times the length of a side of the smaller square. Find the length of a side of the smaller square. __________ inches

Use the difference of squares pattern to factor the polynomial. x2−49x ^ { 2 } - 49x2−49

Factor the following trinomial completely. x2+16x+63x ^ { 2 } + 16 x + 63x2+16x+63

Solve the equation. (p−8)(p+1)=−20( p - 8 ) ( p + 1 ) = - 20(p−8)(p+1)=−20

Factor the polynomial completely. 64−25m264 - 25 m ^ { 2 }64−25m2

An apple orchard contains 66 trees. The number of trees per row is five more than the number of rows. Find the number of rows.

Use the process of factoring by grouping to factor the polynomial. 2z2+z−10z−52 z ^ { 2 } + z - 10 z - 52z2+z−10z−5

Factor the following perfect square trinomial. 64a2−48an+9n264 a ^ { 2 } - 48 a n + 9 n ^ { 2 }64a2−48an+9n2

Factor the following polynomial completely. 3a4−2433 a ^ { 4 } - 2433a4−243

Solve the equation. 3x2=8673 x ^ { 2 } = 8673x2=867 Please enter your answer as two numbers, separated by a comma.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Factor the polynomial completely. $4 a ^ { 4 } + 25 a ^ { 2 }$

Solve the equation. $x ^ { 2 } + 25 x + 154$ = 0 Please enter your answer as two numbers, separated by a comma.

Factor the following trinomial assuming that all variables appearing as exponents represent positive integers. $x ^ { 2 a } + 10 x ^ { a } + 21$

Solve the equation. $- x ^ { 2 } - 6 x + 7 = 0$ Please enter your answer as two numbers, separated by a comma.

Solve the equation. $20 x ^ { 2 } + 43 x = - 14$

Factor this trinomial completely. $10 x ^ { 2 } - 11 x y - 6 y ^ { 2 }$

Solve the equation. $( u - 8 ) ( u + 2 ) = - 24$ Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. $14 x ^ { 2 } - 52 x + 30$

Factor the following perfect square trinomial. $b ^ { 2 } + 4 b + 4$

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 49$

Factor the following trinomial completely. $x ^ { 2 } + 16 x + 63$

Solve the equation. $( p - 8 ) ( p + 1 ) = - 20$

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

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 10 z - 5$

Factor the following perfect square trinomial. $64 a ^ { 2 } - 48 a n + 9 n ^ { 2 }$

Factor the following polynomial completely. $3 a ^ { 4 } - 243$

Solve the equation. $3 x ^ { 2 } = 867$ Please enter your answer as two numbers, separated by a comma.