Question 1

Factor the trinomial completely. $6 x ^ { 2 } + 29 x y + 28 y ^ { 2 }$

Accepted Answer

A)  (2 x $-$ 7 y )(3 x $-$ 4 y ) 
B)  (2 x + 7 y )(3 x + 4 y ) 
C)  (2 x + 7 y )(3 x $-$ 4 y ) 
D)  (2 x $-$ 7 y )(3 x + 4 y ) 
E)  not factorable 
A)  (2 x $-$ 7 y )(3 x $-$ 4 y ) 
B)  (2 x + 7 y )(3 x + 4 y ) 
C)  (2 x + 7 y )(3 x $-$ 4 y ) 
D)  (2 x $-$ 7 y )(3 x + 4 y ) 
E)  not factorable

Question 2

Factor the trinomial completely. $28 x ^ { 2 } + 13 x y - 6 y ^ { 2 }$

Accepted Answer

A)  (4 x + 3 y )(7 x + 2 y ) 
B)  (4 x $-$ 3 y )(7 x + 2 y ) 
C)  (4 x $-$ 3 y )(7 x $-$ 2 y ) 
D)  (4 x + 3 y )(7 x $-$ 2 y ) 
E)  not factorable 
A)  (4 x + 3 y )(7 x + 2 y ) 
B)  (4 x $-$ 3 y )(7 x + 2 y ) 
C)  (4 x $-$ 3 y )(7 x $-$ 2 y ) 
D)  (4 x + 3 y )(7 x $-$ 2 y ) 
E)  not factorable

Question 3

Factor the polynomial completely. $3 x ^ { 7 } + 3 x ^ { 8 } + 3 x ^ { 5 }$

Accepted Answer

A)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + 3 \right)$ 
B)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + x \right)$ 
C)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 4 } + x \right)$ 
D)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } \right)$ 
E)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + 1 \right)$ 
A)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + 3 \right)$ 
B)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + x \right)$ 
C)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 4 } + x \right)$ 
D)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } \right)$ 
E)  $3 x ^ { 5 } \left( x ^ { 2 } + x ^ { 3 } + 1 \right)$

Question 4

Solve the equation. $t ^ { 3 } - 2 t ^ { 2 } - 3 t = 0$ Please enter your answer as three numbers, separated by commas.

Accepted Answer

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

Question 5

Factor the trinomial completely. Indicate if it is not factorable using integers. $7 n ^ { 2 } + 2 n - 3$

Accepted Answer

A)  $( n + 3 ) ( 7 n - 1 )$ 
B)  $( 7 n + 3 ) ( n - 1 )$ 
C)  $( 7 n - 3 ) ( n + 1 )$ 
D)  $( n - 3 ) ( 7 n + 1 )$ 
E)  not factorable 
A)  $( n + 3 ) ( 7 n - 1 )$ 
B)  $( 7 n + 3 ) ( n - 1 )$ 
C)  $( 7 n - 3 ) ( n + 1 )$ 
D)  $( n - 3 ) ( 7 n + 1 )$ 
E)  not factorable

Question 6

Using a systematic technique to factor a trinomial of the form $a x ^ { 2 } + b x + c$ , find two factors of ac that sum to b .

Accepted Answer

A) True 
 B)False

Question 7

Solve the equation. $( 10 u - 1 ) ( 6 u - 5 ) = 0$

Accepted Answer

A)  $\left\{ \frac { 1 } { 10 } , - \frac { 5 } { 6 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 10 } , \frac { 5 } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } , \frac { 5 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 10 } , - \frac { 5 } { 6 } \right\}$ 
E)  none of these 
A)  $\left\{ \frac { 1 } { 10 } , - \frac { 5 } { 6 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 10 } , \frac { 5 } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 10 } , \frac { 5 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 10 } , - \frac { 5 } { 6 } \right\}$ 
E)  none of these

Question 8

Factor this trinomial completely. $9 y ^ { 2 } + y + 2$ Enter none if the trinomial is not factorable.

Accepted Answer

The answer of Factor this trinomial completely. \(9 y ^...

Question 9

The area of a rectangle is 6 times the area of a square. If the rectangle is 24 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square. __________ inches

Accepted Answer

The answer of The area of a rectangle is 6...

Question 10

Solve the equation. $x ( x - 10 ) = - 24$

Accepted Answer

A)  {-4, 6} 
B)  {10, -24} 
C)  {4, -6} 
D)  {-4, -6} 
E)  {4, 6} 
A)  {-4, 6} 
B)  {10, -24} 
C)  {4, -6} 
D)  {-4, -6} 
E)  {4, 6}

Question 11

Solve the equation. $15 y ^ { 2 } = - 45 y$ Please enter your answer as two numbers, separated by a comma.

Accepted Answer

The answer of Solve the equation. \(15 y ^ {...

Question 12

Find which of the following trinomials is not factorable using integers. Match the trinomials to factorable and not factorable .
-not factorable

Accepted Answer

A)  $t ^ { 2 } + 12 t + 24$ 
B)  $x ^ { 2 } - 10 x + 21$ 
A)  $t ^ { 2 } + 12 t + 24$ 
B)  $x ^ { 2 } - 10 x + 21$

Question 13

The square of a number equals 20 times that number. Find the number.

Accepted Answer

A)  1 
B)  $-$ 20 or 0 
C)  20 or 0 
D)  1 or 20 
E)  $-$ 20 or 1 
A)  1 
B)  $-$ 20 or 0 
C)  20 or 0 
D)  1 or 20 
E)  $-$ 20 or 1

Question 14

The area of a rectangle is 15 times the area of a square. If the rectangle is 75 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

Accepted Answer

A)  5 inches 
B)  15 inches 
C)  10 inches 
D)  3 inches 
E)  7 inches 
A)  5 inches 
B)  15 inches 
C)  10 inches 
D)  3 inches 
E)  7 inches

Question 15

The area of a triangle is 20 square inches. One side of the triangle is 7 inches less than three times the length of the altitude to that side. Find the length of that side.

Accepted Answer

A)  9 in. 
B)  10 in. 
C)  6 in. 
D)  8 in. 
A)  9 in. 
B)  10 in. 
C)  6 in. 
D)  8 in.

Question 16

A trinomial of the form $a x ^ { 2 } + b x + c$ will always have a common factor other than 1.

Accepted Answer

A) True 
 B)False

Question 17

The equation $x ^ { 2 } - 7 x = - 49$ is not factorable because it is equal to a negative number.

Accepted Answer

A) True 
 B)False

Question 18

Suppose that the area of a circle is numerically equal to 25 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. Leave $\pi$ in your answer. Please enter your answer as a fraction.

Accepted Answer

The answer of Suppose that the area of a circle...

Question 19

Factor the following polynomial completely. $4 m ^ { 3 } - 64 m ^ { 3 }$

Accepted Answer

A)  $4 m ( m - 4 ) ( m + 4 )$ 
B)  $4 m \left( m ^ { 2 } + 16 \right)$ 
C)  $4 m ( m - 4 ) ( m - 4 )$ 
D)  none of these 
A)  $4 m ( m - 4 ) ( m + 4 )$ 
B)  $4 m \left( m ^ { 2 } + 16 \right)$ 
C)  $4 m ( m - 4 ) ( m - 4 )$ 
D)  none of these

Question 20

Factor the trinomial completely. Indicate if it is not factorable using integers. $10 x ^ { 2 } + 37 x + 7$

Accepted Answer

( 5 x + 1

Factor the trinomial completely. $6 x ^ { 2 } + 29 x y + 28 y ^ { 2 }$

Factor the trinomial completely. $28 x ^ { 2 } + 13 x y - 6 y ^ { 2 }$

Factor the polynomial completely. $3 x ^ { 7 } + 3 x ^ { 8 } + 3 x ^ { 5 }$

Solve the equation. $t ^ { 3 } - 2 t ^ { 2 } - 3 t = 0$ Please enter your answer as three numbers, separated by commas.

Factor the trinomial completely. Indicate if it is not factorable using integers. $7 n ^ { 2 } + 2 n - 3$

Using a systematic technique to factor a trinomial of the form $a x ^ { 2 } + b x + c$ , find two factors of ac that sum to b .

Solve the equation. $( 10 u - 1 ) ( 6 u - 5 ) = 0$

Factor this trinomial completely. $9 y ^ { 2 } + y + 2$ Enter none if the trinomial is not factorable.

The area of a rectangle is 6 times the area of a square. If the rectangle is 24 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square. __________ inches

Solve the equation. $x ( x - 10 ) = - 24$

Solve the equation. $15 y ^ { 2 } = - 45 y$ Please enter your answer as two numbers, separated by a comma.

Find which of the following trinomials is not factorable using integers. Match the trinomials to factorable and not factorable . -not factorable

The square of a number equals 20 times that number. Find the number.

The area of a rectangle is 15 times the area of a square. If the rectangle is 75 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

The area of a triangle is 20 square inches. One side of the triangle is 7 inches less than three times the length of the altitude to that side. Find the length of that side.

A trinomial of the form $a x ^ { 2 } + b x + c$ will always have a common factor other than 1.

The equation $x ^ { 2 } - 7 x = - 49$ is not factorable because it is equal to a negative number.

Suppose that the area of a circle is numerically equal to 25 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. Leave $\pi$ in your answer. Please enter your answer as a fraction.

Factor the following polynomial completely. $4 m ^ { 3 } - 64 m ^ { 3 }$

Factor the trinomial completely. Indicate if it is not factorable using integers. $10 x ^ { 2 } + 37 x + 7$

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 trinomial completely. 6x2+29xy+28y26 x ^ { 2 } + 29 x y + 28 y ^ { 2 }6x2+29xy+28y2

Factor the trinomial completely. 28x2+13xy−6y228 x ^ { 2 } + 13 x y - 6 y ^ { 2 }28x2+13xy−6y2

Factor the polynomial completely. 3x7+3x8+3x53 x ^ { 7 } + 3 x ^ { 8 } + 3 x ^ { 5 }3x7+3x8+3x5

Solve the equation. t3−2t2−3t=0t ^ { 3 } - 2 t ^ { 2 } - 3 t = 0t3−2t2−3t=0 Please enter your answer as three numbers, separated by commas.

Factor the trinomial completely. Indicate if it is not factorable using integers. 7n2+2n−37 n ^ { 2 } + 2 n - 37n2+2n−3

Using a systematic technique to factor a trinomial of the form ax2+bx+ca x ^ { 2 } + b x + cax2+bx+c , find two factors of ac that sum to b .

Solve the equation. (10u−1)(6u−5)=0( 10 u - 1 ) ( 6 u - 5 ) = 0(10u−1)(6u−5)=0

Factor this trinomial completely. 9y2+y+29 y ^ { 2 } + y + 29y2+y+2 Enter none if the trinomial is not factorable.

The area of a rectangle is 6 times the area of a square. If the rectangle is 24 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square. __________ inches

Solve the equation. x(x−10)=−24x ( x - 10 ) = - 24x(x−10)=−24

Solve the equation. 15y2=−45y15 y ^ { 2 } = - 45 y15y2=−45y Please enter your answer as two numbers, separated by a comma.

Find which of the following trinomials is not factorable using integers. Match the trinomials to factorable and not factorable . -not factorable

The square of a number equals 20 times that number. Find the number.

The area of a rectangle is 15 times the area of a square. If the rectangle is 75 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

The area of a triangle is 20 square inches. One side of the triangle is 7 inches less than three times the length of the altitude to that side. Find the length of that side.

A trinomial of the form ax2+bx+ca x ^ { 2 } + b x + cax2+bx+c will always have a common factor other than 1.

The equation x2−7x=−49x ^ { 2 } - 7 x = - 49x2−7x=−49 is not factorable because it is equal to a negative number.

Suppose that the area of a circle is numerically equal to 25 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. Leave π\piπ in your answer. Please enter your answer as a fraction.

Factor the following polynomial completely. 4m3−64m34 m ^ { 3 } - 64 m ^ { 3 }4m3−64m3

Factor the trinomial completely. Indicate if it is not factorable using integers. 10x2+37x+710 x ^ { 2 } + 37 x + 710x2+37x+7

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 trinomial completely. $6 x ^ { 2 } + 29 x y + 28 y ^ { 2 }$

Factor the trinomial completely. $28 x ^ { 2 } + 13 x y - 6 y ^ { 2 }$

Factor the polynomial completely. $3 x ^ { 7 } + 3 x ^ { 8 } + 3 x ^ { 5 }$

Solve the equation. $t ^ { 3 } - 2 t ^ { 2 } - 3 t = 0$ Please enter your answer as three numbers, separated by commas.

Factor the trinomial completely. Indicate if it is not factorable using integers. $7 n ^ { 2 } + 2 n - 3$

Using a systematic technique to factor a trinomial of the form $a x ^ { 2 } + b x + c$ , find two factors of ac that sum to b .

Solve the equation. $( 10 u - 1 ) ( 6 u - 5 ) = 0$

Factor this trinomial completely. $9 y ^ { 2 } + y + 2$ Enter none if the trinomial is not factorable.

Solve the equation. $x ( x - 10 ) = - 24$

Solve the equation. $15 y ^ { 2 } = - 45 y$ Please enter your answer as two numbers, separated by a comma.

A trinomial of the form $a x ^ { 2 } + b x + c$ will always have a common factor other than 1.

The equation $x ^ { 2 } - 7 x = - 49$ is not factorable because it is equal to a negative number.

Suppose that the area of a circle is numerically equal to 25 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. Leave $\pi$ in your answer. Please enter your answer as a fraction.

Factor the following polynomial completely. $4 m ^ { 3 } - 64 m ^ { 3 }$

Factor the trinomial completely. Indicate if it is not factorable using integers. $10 x ^ { 2 } + 37 x + 7$