Question 1

Factor the polynomial completely. $10 p ^ { 5 } c ^ { 4 } + 16 p c ^ { 8 } + 26 p c ^ { 4 }$

Accepted Answer

A)  $2 p c ^ { 4 } \left( 5 p c ^ { 4 } + 8 c ^ { 8 } + 13 \right)$ 
B)  $2 p c ^ { 4 } \left( 5 p ^ { 4 } + 8 c ^ { 4 } + 13 \right)$ 
C)  $2 p c ^ { 4 } \left( 5 c p ^ { 4 } + 8 c ^ { 4 } + 13 \right)$ 
D)  $2 p c ^ { 4 } \left( 5 p c ^ { 4 } + 8 c ^ { 4 } + 13 p \right)$ 
A)  $2 p c ^ { 4 } \left( 5 p c ^ { 4 } + 8 c ^ { 8 } + 13 \right)$ 
B)  $2 p c ^ { 4 } \left( 5 p ^ { 4 } + 8 c ^ { 4 } + 13 \right)$ 
C)  $2 p c ^ { 4 } \left( 5 c p ^ { 4 } + 8 c ^ { 4 } + 13 \right)$ 
D)  $2 p c ^ { 4 } \left( 5 p c ^ { 4 } + 8 c ^ { 4 } + 13 p \right)$

Question 2

Set up an equation and solve the problem. The difference of the areas of two squares is 288 square inches. Each side of the larger square is 3 times the length of a side of the smaller square. Find the length of a side of the larger square.

Accepted Answer

A)  6 in. 
B)  18 in. 
C)  3 in. 
D)  9 in. 
E)  none of these 
A)  6 in. 
B)  18 in. 
C)  3 in. 
D)  9 in. 
E)  none of these

Question 3

Find the greatest common factor of the given expression. $7 p \text { and } 77 p c$

Accepted Answer

The answer of Find the greatest common factor of the...

Question 4

Suppose that one leg of a right triangle is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

Accepted Answer

A)  6 feet, 16 feet, 18 feet 
B)  6 feet, 17 feet, 18 feet 
C)  10 feet, 17 feet, 19 feet 
D)  8 feet, 15 feet, 17 feet 
E)  9 feet, 16 feet, 18 feet 
A)  6 feet, 16 feet, 18 feet 
B)  6 feet, 17 feet, 18 feet 
C)  10 feet, 17 feet, 19 feet 
D)  8 feet, 15 feet, 17 feet 
E)  9 feet, 16 feet, 18 feet

Question 5

Given $x ^ { 2 } + b x + c$ , if no two factors of c produce a sum of b , then the trinomial is not factorable using integers.

Accepted Answer

A) True 
 B)False

Question 6

Factor the polynomial completely. $28 x + 8 c$

Accepted Answer

The answer of Factor the polynomial completely. \(28 x +...

Question 7

The sum of the areas of two circles is $290 \pi$ square inches. The length of a radius of the smaller circle is 2 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle.

Accepted Answer

A)  15 in. 
B)  11 in. 
C)  13 in. 
D)  12 in. 
A)  15 in. 
B)  11 in. 
C)  13 in. 
D)  12 in.

Question 8

Perfect-square-trinomial equations such as $a ^ { 2 } + 2 a b + b ^ { 2 } = 0$ will have one unique solution.

Accepted Answer

A) True 
 B)False

Question 9

Find three negative consecutive integers such that the product of the two smaller integers is 50 more than ten times the largest integer. Please enter your answer as three numbers, separated by a comma.

Accepted Answer

The answer of Find three negative consecutive integers such that...

Question 10

Solve the equation. $m ^ { 2 } + 7 m + 10 = 0$ If there is more than one solution, separate your answers with commas.

Accepted Answer

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

Question 11

The difference-of-squares pattern may be used only once when solving a word problem.

Accepted Answer

A) True 
 B)False

Question 12

To factor a trinomial of the form $a x ^ { 2 } + b x + c$ , the trial and error technique is the preferred method.

Accepted Answer

A) True 
 B)False

Question 13

Find the greatest common factor of the given expressions. $54 y ^ { 4 } a ^ { 9 } , 48 y ^ { 3 } a ^ { 11 } \text { and } 78 y ^ { 6 } a ^ { 5 }$

Accepted Answer

A)  $8 a ^ { 9 }$ 
B)  $6 y ^ { 3 } a ^ { 5 }$ 
C)  $9 y ^ { 8 } a ^ { 5 }$ 
D)  $8 a ^ { 8 }$ 
E)  $6 y a ^ { 10 }$ 
A)  $8 a ^ { 9 }$ 
B)  $6 y ^ { 3 } a ^ { 5 }$ 
C)  $9 y ^ { 8 } a ^ { 5 }$ 
D)  $8 a ^ { 8 }$ 
E)  $6 y a ^ { 10 }$

Question 14

Solve the equation. $x ( x - 10 ) = - 9$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

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

Question 15

Factor the trinomial completely. Indicate if it is not factorable using integers. $10 x ^ { 2 } + 33 x - 7$

Accepted Answer

A)  $( 5 x - 1 ) ( 2 x - 7 )$ 
B)  $( 5 x + 1 ) ( 2 x - 7 )$ 
C)  $( 5 x - 1 ) ( 2 x + 7 )$ 
D)  $( 5 x - 7 ) ( 2 x - 1 )$ 
E)  not factorable 
A)  $( 5 x - 1 ) ( 2 x - 7 )$ 
B)  $( 5 x + 1 ) ( 2 x - 7 )$ 
C)  $( 5 x - 1 ) ( 2 x + 7 )$ 
D)  $( 5 x - 7 ) ( 2 x - 1 )$ 
E)  not factorable

Question 16

Choose the correct solution set. $20 y ^ { 2 } + 13 y - 21 = 0$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 5 } , \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 } { 5 } , - \frac { 3 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 7 } , \frac { 4 } { 3 } \right\}$ 
D)  $\left\{ \frac { 7 } { 5 } , - \frac { 4 } { 3 } \right\}$ 
E)  $\left\{ \frac { 7 } { 5 } , \frac { 3 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 5 } , \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 7 } { 5 } , - \frac { 3 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 7 } , \frac { 4 } { 3 } \right\}$ 
D)  $\left\{ \frac { 7 } { 5 } , - \frac { 4 } { 3 } \right\}$ 
E)  $\left\{ \frac { 7 } { 5 } , \frac { 3 } { 4 } \right\}$

Question 17

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 10 inches in order to reduce the size of the paper to an area of 4 square inches. Find the width of the strip.

Accepted Answer

A)  5.0 in. 
B)  3.5 in. 
C)  4.0 in. 
D)  4.5 in. 
A)  5.0 in. 
B)  3.5 in. 
C)  4.0 in. 
D)  4.5 in.

Question 18

Suppose that the area of a circle is numerically equal to 12 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square.

Accepted Answer

A)  $\frac { \pi } { 48 }$ 
B)  $\frac { 48 } { \pi }$ 
C)  $48 \pi$ 
A)  $\frac { \pi } { 48 }$ 
B)  $\frac { 48 } { \pi }$ 
C)  $48 \pi$

Question 19

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $2 x ^ { 2 } - 32 y ^ { 2 }$

Accepted Answer

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

Question 20

Factor the following perfect square trinomial. $16 x ^ { 2 } + 8 x + 1$

Accepted Answer

The answer of Factor the following perfect square trinomial. \(16...

Factor the polynomial completely. $10 p ^ { 5 } c ^ { 4 } + 16 p c ^ { 8 } + 26 p c ^ { 4 }$

Set up an equation and solve the problem. The difference of the areas of two squares is 288 square inches. Each side of the larger square is 3 times the length of a side of the smaller square. Find the length of a side of the larger square.

Find the greatest common factor of the given expression. $7 p \text { and } 77 p c$

Suppose that one leg of a right triangle is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

Given $x ^ { 2 } + b x + c$ , if no two factors of c produce a sum of b , then the trinomial is not factorable using integers.

Factor the polynomial completely. $28 x + 8 c$

The sum of the areas of two circles is $290 \pi$ square inches. The length of a radius of the smaller circle is 2 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle.

Perfect-square-trinomial equations such as $a ^ { 2 } + 2 a b + b ^ { 2 } = 0$ will have one unique solution.

Find three negative consecutive integers such that the product of the two smaller integers is 50 more than ten times the largest integer. Please enter your answer as three numbers, separated by a comma.

Solve the equation. $m ^ { 2 } + 7 m + 10 = 0$ If there is more than one solution, separate your answers with commas.

The difference-of-squares pattern may be used only once when solving a word problem.

To factor a trinomial of the form $a x ^ { 2 } + b x + c$ , the trial and error technique is the preferred method.

Find the greatest common factor of the given expressions. $54 y ^ { 4 } a ^ { 9 } , 48 y ^ { 3 } a ^ { 11 } \text { and } 78 y ^ { 6 } a ^ { 5 }$

Solve the equation. $x ( x - 10 ) = - 9$ Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. $10 x ^ { 2 } + 33 x - 7$

Choose the correct solution set. $20 y ^ { 2 } + 13 y - 21 = 0$

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 10 inches in order to reduce the size of the paper to an area of 4 square inches. Find the width of the strip.

Suppose that the area of a circle is numerically equal to 12 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square.

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $2 x ^ { 2 } - 32 y ^ { 2 }$

Factor the following perfect square trinomial. $16 x ^ { 2 } + 8 x + 1$

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. 10p5c4+16pc8+26pc410 p ^ { 5 } c ^ { 4 } + 16 p c ^ { 8 } + 26 p c ^ { 4 }10p5c4+16pc8+26pc4

Set up an equation and solve the problem. The difference of the areas of two squares is 288 square inches. Each side of the larger square is 3 times the length of a side of the smaller square. Find the length of a side of the larger square.

Find the greatest common factor of the given expression. 7p and 77pc7 p \text { and } 77 p c7p and 77pc

Suppose that one leg of a right triangle is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the lengths of all three sides of the right triangle.

Given x2+bx+cx ^ { 2 } + b x + cx2+bx+c , if no two factors of c produce a sum of b , then the trinomial is not factorable using integers.

Factor the polynomial completely. 28x+8c28 x + 8 c28x+8c

The sum of the areas of two circles is 290π290 \pi290π square inches. The length of a radius of the smaller circle is 2 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle.

Perfect-square-trinomial equations such as a2+2ab+b2=0a ^ { 2 } + 2 a b + b ^ { 2 } = 0a2+2ab+b2=0 will have one unique solution.

Find three negative consecutive integers such that the product of the two smaller integers is 50 more than ten times the largest integer. Please enter your answer as three numbers, separated by a comma.

Solve the equation. m2+7m+10=0m ^ { 2 } + 7 m + 10 = 0m2+7m+10=0 If there is more than one solution, separate your answers with commas.

The difference-of-squares pattern may be used only once when solving a word problem.

To factor a trinomial of the form ax2+bx+ca x ^ { 2 } + b x + cax2+bx+c , the trial and error technique is the preferred method.

Find the greatest common factor of the given expressions. 54y4a9,48y3a11 and 78y6a554 y ^ { 4 } a ^ { 9 } , 48 y ^ { 3 } a ^ { 11 } \text { and } 78 y ^ { 6 } a ^ { 5 }54y4a9,48y3a11 and 78y6a5

Solve the equation. x(x−10)=−9x ( x - 10 ) = - 9x(x−10)=−9 Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. 10x2+33x−710 x ^ { 2 } + 33 x - 710x2+33x−7

Choose the correct solution set. 20y2+13y−21=020 y ^ { 2 } + 13 y - 21 = 020y2+13y−21=0

A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 13 inches by 10 inches in order to reduce the size of the paper to an area of 4 square inches. Find the width of the strip.

Suppose that the area of a circle is numerically equal to 12 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square.

Factor the polynomial completely. Don t forget to look for a common monomial factor first. 2x2−32y22 x ^ { 2 } - 32 y ^ { 2 }2x2−32y2

Factor the following perfect square trinomial. 16x2+8x+116 x ^ { 2 } + 8 x + 116x2+8x+1

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. $10 p ^ { 5 } c ^ { 4 } + 16 p c ^ { 8 } + 26 p c ^ { 4 }$

Find the greatest common factor of the given expression. $7 p \text { and } 77 p c$

Given $x ^ { 2 } + b x + c$ , if no two factors of c produce a sum of b , then the trinomial is not factorable using integers.

Factor the polynomial completely. $28 x + 8 c$

The sum of the areas of two circles is $290 \pi$ square inches. The length of a radius of the smaller circle is 2 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle.

Perfect-square-trinomial equations such as $a ^ { 2 } + 2 a b + b ^ { 2 } = 0$ will have one unique solution.

Solve the equation. $m ^ { 2 } + 7 m + 10 = 0$ If there is more than one solution, separate your answers with commas.

To factor a trinomial of the form $a x ^ { 2 } + b x + c$ , the trial and error technique is the preferred method.

Find the greatest common factor of the given expressions. $54 y ^ { 4 } a ^ { 9 } , 48 y ^ { 3 } a ^ { 11 } \text { and } 78 y ^ { 6 } a ^ { 5 }$

Solve the equation. $x ( x - 10 ) = - 9$ Please enter your answer as two numbers, separated by a comma.

Factor the trinomial completely. Indicate if it is not factorable using integers. $10 x ^ { 2 } + 33 x - 7$

Choose the correct solution set. $20 y ^ { 2 } + 13 y - 21 = 0$

Factor the polynomial completely. Don t forget to look for a common monomial factor first. $2 x ^ { 2 } - 32 y ^ { 2 }$

Factor the following perfect square trinomial. $16 x ^ { 2 } + 8 x + 1$