Question 1

Perform the indicated operations and simplify. $- \left( - 5 x ^ { 2 } + 3 x + 17 \right) - \left( 3 x - 5 x ^ { 2 } + 17 \right)$ .

Accepted Answer

A)  $10 x ^ { 2 } - 6 x - 34$ 
B) 0 
C) -34 
D)  $- 6 x - 34$ 
E)  $10 x ^ { 2 } - 34$ 
A)  $10 x ^ { 2 } - 6 x - 34$ 
B) 0 
C) -34 
D)  $- 6 x - 34$ 
E)  $10 x ^ { 2 } - 34$

Question 2

Factor out the greatest common monomial factor of the polynomial below, if one exists. $y ^ { 2 } + 9 y$

Accepted Answer

A)  $y ^ { 2 } ( y + 9 )$ 
B)  $y ( y + 9 ) ( y + 1 )$ 
C)  $y ( y + 9 )$ 
D)  $y ( y + 9 ) ^ { 2 }$ 
E) no common factor other than 1 
A)  $y ^ { 2 } ( y + 9 )$ 
B)  $y ( y + 9 ) ( y + 1 )$ 
C)  $y ( y + 9 )$ 
D)  $y ( y + 9 ) ^ { 2 }$ 
E) no common factor other than 1

Question 3

Use the Zero-Factor Property to solve the equation below. $x ( x + 6 ) = 0$

Accepted Answer

A)  $x = 0$ and $x = 6$ 
B)  $x = - 6$ 
C)  $x = - 6$ and $x = 0$ 
D)  $x = 0$ 
E)  $x = 6$ 
A)  $x = 0$ and $x = 6$ 
B)  $x = - 6$ 
C)  $x = - 6$ and $x = 0$ 
D)  $x = 0$ 
E)  $x = 6$

Question 4

Evaluate the expression $\frac { 2.6 \times 10 ^ { 5 } } { 1.3 \times 10 ^ { 3 } }$ . Write the answer in scientific notation.

Accepted Answer

A)  $2 \times 10 ^ { 4 }$ 
B)  $2 \times 10 ^ { 1 }$ 
C)  $2 \times 10 ^ { 2 }$ 
D)  $2 \times 10 ^ { 3 }$ 
E)  $2 \times 10 ^ { - 2 }$ 
A)  $2 \times 10 ^ { 4 }$ 
B)  $2 \times 10 ^ { 1 }$ 
C)  $2 \times 10 ^ { 2 }$ 
D)  $2 \times 10 ^ { 3 }$ 
E)  $2 \times 10 ^ { - 2 }$

Question 5

Fill in the missing factor. $6 x ^ { 2 } + 27 x = 3 x ( - )$

Accepted Answer

A)  2x+9 
B)  $2 x ^ { 2 } + 3$ 
C)  $x ^ { 2 } + 27$ 
D)  3x+1 
E)  2x+27 
A)  2x+9 
B)  $2 x ^ { 2 } + 3$ 
C)  $x ^ { 2 } + 27$ 
D)  3x+1 
E)  2x+27

Question 6

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. 
$\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$

Accepted Answer

A)  $\frac { b ^ { 3 } } { 5 a ^ { 25 } }$ 
B)  $\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }$ 
C)  $\frac { b ^ { 3 } } { 5 a ^ { 24 } }$ 
D)  $\frac { b ^ { 2 } } { 5 a ^ { 24 } }$ 
E)  $\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }$ 
A)  $\frac { b ^ { 3 } } { 5 a ^ { 25 } }$ 
B)  $\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }$ 
C)  $\frac { b ^ { 3 } } { 5 a ^ { 24 } }$ 
D)  $\frac { b ^ { 2 } } { 5 a ^ { 24 } }$ 
E)  $\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }$

Question 7

Find the difference $( - 9 x + 8 ) - ( 2 x + 4 )$ .

Accepted Answer

A)  -11 x+2 
B)  -7x+12 
C)  $- 7 x ^ { 2 } + 12$ 
D)  -11 x+4 
E)  $- 7 x ^ { 2 } + 4$ 
A)  -11 x+2 
B)  -7x+12 
C)  $- 7 x ^ { 2 } + 12$ 
D)  -11 x+4 
E)  $- 7 x ^ { 2 } + 4$

Question 8

Solve the equation below by factoring. $$x ( x + 7 ) - 5 ( x + 7 ) = 0$$

Accepted Answer

A)  $0,35$ 
B)  $- 7,35$ 
C)  $- 7,5$ 
D)  $7,5$ 
E)  $7 , - 5$ 
A)  $0,35$ 
B)  $- 7,35$ 
C)  $- 7,5$ 
D)  $7,5$ 
E)  $7 , - 5$

Question 9

Find the height in feet of a free-falling object at time t=5 using the function $s = - 16 t ^ { 2 } + 76 t + 118$ .

Accepted Answer

A) 138 feet 
B) 98 feet 
C) 20 feet 
D) 662 feet 
E) 898 feet 
A) 138 feet 
B) 98 feet 
C) 20 feet 
D) 662 feet 
E) 898 feet

Question 10

Use a special product formula to find the product. $( 0.1 x + 0.4 ) ( 0.1 x - 0.4 )$

Accepted Answer

A)  $0.01 x ^ { 2 } - 0.16$ 
B)  $0.01 x ^ { 2 } - 0.08 x + 0.16$ 
C)  $0.01 x ^ { 2 } + 0.16$ 
D)  $0.01 x ^ { 2 } + 0.08 x - 0.16$ 
E)  $0.01 x ^ { 2 } - 0.04 x + 0.16$ 
A)  $0.01 x ^ { 2 } - 0.16$ 
B)  $0.01 x ^ { 2 } - 0.08 x + 0.16$ 
C)  $0.01 x ^ { 2 } + 0.16$ 
D)  $0.01 x ^ { 2 } + 0.08 x - 0.16$ 
E)  $0.01 x ^ { 2 } - 0.04 x + 0.16$

Question 11

Write the polynomial $- 2 x - 6 x ^ { 4 } + 4 x ^ { 2 } + 7$ in standard form. Find the leading coefficient of the polynomial.

Accepted Answer

A)  $7 + 4 x ^ { 2 } - 2 x - 6 x ^ { 4 }$ leading coefficient: 2 
B)  $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 7 
C)  $7 + 4 x ^ { 2 } - 2 x - 6 x ^ { 4 }$ leading coefficient: 7 
D)  $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 6 
E)  $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 2 
A)  $7 + 4 x ^ { 2 } - 2 x - 6 x ^ { 4 }$ leading coefficient: 2 
B)  $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 7 
C)  $7 + 4 x ^ { 2 } - 2 x - 6 x ^ { 4 }$ leading coefficient: 7 
D)  $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 6 
E)  $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 2

Question 12

Solve the equation below by factoring. $$c ^ { 3 } + 2 c ^ { 2 } - 4 c - 8 = 0$$

Accepted Answer

A)  $c = 0$ and $c = 2$ 
B)  $c = - 2$ , $c = 0$ , and $c = 2$ 
C)  $c = - 2$ 
D)  $c = - 2$ and $c = 2$ 
E)  $c = - 2$ and $c = 0$ 
A)  $c = 0$ and $c = 2$ 
B)  $c = - 2$ , $c = 0$ , and $c = 2$ 
C)  $c = - 2$ 
D)  $c = - 2$ and $c = 2$ 
E)  $c = - 2$ and $c = 0$

Question 13

Write, in factored form, an expression for the area of the constructed figure below if A is unknown and B is equal to $6$ .

Accepted Answer

A)  $A ( A + 6 )$ 
B)  $( A - 6 ) ^ { 2 }$ 
C)  $( A + 6 ) ^ { 2 }$ 
D)  $( A + 6 ) ( A - 6 )$ 
E)  $A ( A - 6 )$ 
A)  $A ( A + 6 )$ 
B)  $( A - 6 ) ^ { 2 }$ 
C)  $( A + 6 ) ^ { 2 }$ 
D)  $( A + 6 ) ( A - 6 )$ 
E)  $A ( A - 6 )$

Question 14

Fill in the missing factor. $x ^ { 2 } + 5 x + 6 = ( x + 2 ) ( - )$

Accepted Answer

A)  x-3 
B)  3-x 
C)   x+3 
D)   3+x 
E)  3x 
A)  x-3 
B)  3-x 
C)   x+3 
D)   3+x 
E)  3x

Question 15

Factor the difference of cubes. $t ^ { 3 } - 8$

Accepted Answer

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

Question 16

Add $5 z - 4 z ^ { 2 } \text { to } 6 z ^ { 2 } + 6 z$ .

Accepted Answer

A)  $11 z ^ { 4 } + 2 z ^ { 2 }$ 
B)  $13 z ^ { 6 }$ 
C)  $2 z ^ { 2 } + 11 z$ 
D)  $11 z ^ { 2 } + 2 z$ 
E)  $2 z ^ { 4 } + 11 z ^ { 2 }$ 
A)  $11 z ^ { 4 } + 2 z ^ { 2 }$ 
B)  $13 z ^ { 6 }$ 
C)  $2 z ^ { 2 } + 11 z$ 
D)  $11 z ^ { 2 } + 2 z$ 
E)  $2 z ^ { 4 } + 11 z ^ { 2 }$

Question 17

A triangle has an area of 45 square inches. The height of the triangle is 2 $\frac { 1 } { 2 }$ times its base. Find the height of the triangle.

Accepted Answer

A) 11 inches 
B) 30 inches 
C) 15 inches 
D) 21 inches 
E) 90 inches 
A) 11 inches 
B) 30 inches 
C) 15 inches 
D) 21 inches 
E) 90 inches

Question 18

Factor completely the polynomial below. $3 x ^ { 4 } - 243 x ^ { 2 }$

Accepted Answer

A)  $3 x ^ { 2 } ( x + 9 ) ^ { 2 }$ 
B)  $3 x ^ { 2 } ( x - 9 ) ^ { 2 }$ 
C)  $3 x ( x - 9 ) ^ { 2 } ( x + 9 )$ 
D)  $3 x ( x - 9 ) ( x + 9 ) ^ { 2 }$ 
E)  $3 x ^ { 2 } ( x - 9 ) ( x + 9 )$ 
A)  $3 x ^ { 2 } ( x + 9 ) ^ { 2 }$ 
B)  $3 x ^ { 2 } ( x - 9 ) ^ { 2 }$ 
C)  $3 x ( x - 9 ) ^ { 2 } ( x + 9 )$ 
D)  $3 x ( x - 9 ) ( x + 9 ) ^ { 2 }$ 
E)  $3 x ^ { 2 } ( x - 9 ) ( x + 9 )$

Question 19

Use a special product pattern to find the product $( 7 x + 2 ) ( 7 x - 2 )$ .

Accepted Answer

A)  $49 x ^ { 2 } - 4$ 
B)  $49 x ^ { 2 } - 28 x + 4$ 
C)  $49 x ^ { 2 } + 4$ 
D)  $49 x ^ { 2 } - 9 x - 4$ 
E)  $49 x ^ { 2 } - 14 x + 4$ 
A)  $49 x ^ { 2 } - 4$ 
B)  $49 x ^ { 2 } - 28 x + 4$ 
C)  $49 x ^ { 2 } + 4$ 
D)  $49 x ^ { 2 } - 9 x - 4$ 
E)  $49 x ^ { 2 } - 14 x + 4$

Question 20

Find the difference $- 2 - \left( - 6 u ^ { 2 } - 8 \right)$ .

Accepted Answer

A)  $6 u ^ { 2 } - 10$ 
B)  $6 u ^ { 2 } + 6$ 
C)  $4 u ^ { 2 } - 10$ 
D)  $4 u ^ { 2 } + 6$ 
E)  $- 6 u ^ { 2 } - 10$ 
A)  $6 u ^ { 2 } - 10$ 
B)  $6 u ^ { 2 } + 6$ 
C)  $4 u ^ { 2 } - 10$ 
D)  $4 u ^ { 2 } + 6$ 
E)  $- 6 u ^ { 2 } - 10$

Perform the indicated operations and simplify. $- \left( - 5 x ^ { 2 } + 3 x + 17 \right) - \left( 3 x - 5 x ^ { 2 } + 17 \right)$ .

Factor out the greatest common monomial factor of the polynomial below, if one exists. $y ^ { 2 } + 9 y$

Use the Zero-Factor Property to solve the equation below. $x ( x + 6 ) = 0$

Evaluate the expression $\frac { 2.6 \times 10 ^ { 5 } } { 1.3 \times 10 ^ { 3 } }$ . Write the answer in scientific notation.

Fill in the missing factor. $6 x ^ { 2 } + 27 x = 3 x ( - )$

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. $\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$

Find the difference $( - 9 x + 8 ) - ( 2 x + 4 )$ .

Solve the equation below by factoring. $x ( x + 7 ) - 5 ( x + 7 ) = 0$

Find the height in feet of a free-falling object at time t=5 using the function $s = - 16 t ^ { 2 } + 76 t + 118$ .

Use a special product formula to find the product. $( 0.1 x + 0.4 ) ( 0.1 x - 0.4 )$

Write the polynomial $- 2 x - 6 x ^ { 4 } + 4 x ^ { 2 } + 7$ in standard form. Find the leading coefficient of the polynomial.

Solve the equation below by factoring. $c ^ { 3 } + 2 c ^ { 2 } - 4 c - 8 = 0$

Write, in factored form, an expression for the area of the constructed figure below if A is unknown and B is equal to $6$ .

Fill in the missing factor. $x ^ { 2 } + 5 x + 6 = ( x + 2 ) ( - )$

Factor the difference of cubes. $t ^ { 3 } - 8$

Add $5 z - 4 z ^ { 2 } \text { to } 6 z ^ { 2 } + 6 z$ .

A triangle has an area of 45 square inches. The height of the triangle is 2 $\frac { 1 } { 2 }$ times its base. Find the height of the triangle.

Factor completely the polynomial below. $3 x ^ { 4 } - 243 x ^ { 2 }$

Use a special product pattern to find the product $( 7 x + 2 ) ( 7 x - 2 )$ .

Find the difference $- 2 - \left( - 6 u ^ { 2 } - 8 \right)$ .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

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Exam 5: Polynomials and Factoring

Perform the indicated operations and simplify. −(−5x2+3x+17)−(3x−5x2+17)- \left( - 5 x ^ { 2 } + 3 x + 17 \right) - \left( 3 x - 5 x ^ { 2 } + 17 \right)−(−5x2+3x+17)−(3x−5x2+17) .

Factor out the greatest common monomial factor of the polynomial below, if one exists. y2+9yy ^ { 2 } + 9 yy2+9y

Use the Zero-Factor Property to solve the equation below. x(x+6)=0x ( x + 6 ) = 0x(x+6)=0

Evaluate the expression 2.6×1051.3×103\frac { 2.6 \times 10 ^ { 5 } } { 1.3 \times 10 ^ { 3 } }1.3×1032.6×105​ . Write the answer in scientific notation.

Fill in the missing factor. 6x2+27x=3x(−)6 x ^ { 2 } + 27 x = 3 x ( - )6x2+27x=3x(−)

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. (2a−3b2)3b(10a4b)4\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }(10a4b)4(2a−3b2)3b​

Find the difference (−9x+8)−(2x+4)( - 9 x + 8 ) - ( 2 x + 4 )(−9x+8)−(2x+4) .

Solve the equation below by factoring. x(x+7)−5(x+7)=0x ( x + 7 ) - 5 ( x + 7 ) = 0x(x+7)−5(x+7)=0

Find the height in feet of a free-falling object at time t=5 using the function s=−16t2+76t+118s = - 16 t ^ { 2 } + 76 t + 118s=−16t2+76t+118 .

Use a special product formula to find the product. (0.1x+0.4)(0.1x−0.4)( 0.1 x + 0.4 ) ( 0.1 x - 0.4 )(0.1x+0.4)(0.1x−0.4)

Write the polynomial −2x−6x4+4x2+7- 2 x - 6 x ^ { 4 } + 4 x ^ { 2 } + 7−2x−6x4+4x2+7 in standard form. Find the leading coefficient of the polynomial.

Solve the equation below by factoring. c3+2c2−4c−8=0c ^ { 3 } + 2 c ^ { 2 } - 4 c - 8 = 0c3+2c2−4c−8=0

Write, in factored form, an expression for the area of the constructed figure below if A is unknown and B is equal to 666 .

Fill in the missing factor. x2+5x+6=(x+2)(−)x ^ { 2 } + 5 x + 6 = ( x + 2 ) ( - )x2+5x+6=(x+2)(−)

Factor the difference of cubes. t3−8t ^ { 3 } - 8t3−8

Add 5z−4z2 to 6z2+6z5 z - 4 z ^ { 2 } \text { to } 6 z ^ { 2 } + 6 z5z−4z2 to 6z2+6z .

A triangle has an area of 45 square inches. The height of the triangle is 2 12\frac { 1 } { 2 }21​ times its base. Find the height of the triangle.

Factor completely the polynomial below. 3x4−243x23 x ^ { 4 } - 243 x ^ { 2 }3x4−243x2

Use a special product pattern to find the product (7x+2)(7x−2)( 7 x + 2 ) ( 7 x - 2 )(7x+2)(7x−2) .

Find the difference −2−(−6u2−8)- 2 - \left( - 6 u ^ { 2 } - 8 \right)−2−(−6u2−8) .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Perform the indicated operations and simplify. $- \left( - 5 x ^ { 2 } + 3 x + 17 \right) - \left( 3 x - 5 x ^ { 2 } + 17 \right)$ .

Factor out the greatest common monomial factor of the polynomial below, if one exists. $y ^ { 2 } + 9 y$

Use the Zero-Factor Property to solve the equation below. $x ( x + 6 ) = 0$

Evaluate the expression $\frac { 2.6 \times 10 ^ { 5 } } { 1.3 \times 10 ^ { 3 } }$ . Write the answer in scientific notation.

Fill in the missing factor. $6 x ^ { 2 } + 27 x = 3 x ( - )$

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. $\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$

Find the difference $( - 9 x + 8 ) - ( 2 x + 4 )$ .

Solve the equation below by factoring. $x ( x + 7 ) - 5 ( x + 7 ) = 0$

Find the height in feet of a free-falling object at time t=5 using the function $s = - 16 t ^ { 2 } + 76 t + 118$ .

Use a special product formula to find the product. $( 0.1 x + 0.4 ) ( 0.1 x - 0.4 )$

Write the polynomial $- 2 x - 6 x ^ { 4 } + 4 x ^ { 2 } + 7$ in standard form. Find the leading coefficient of the polynomial.

Solve the equation below by factoring. $c ^ { 3 } + 2 c ^ { 2 } - 4 c - 8 = 0$

Write, in factored form, an expression for the area of the constructed figure below if A is unknown and B is equal to $6$ .

Fill in the missing factor. $x ^ { 2 } + 5 x + 6 = ( x + 2 ) ( - )$

Factor the difference of cubes. $t ^ { 3 } - 8$

Add $5 z - 4 z ^ { 2 } \text { to } 6 z ^ { 2 } + 6 z$ .

A triangle has an area of 45 square inches. The height of the triangle is 2 $\frac { 1 } { 2 }$ times its base. Find the height of the triangle.

Factor completely the polynomial below. $3 x ^ { 4 } - 243 x ^ { 2 }$

Use a special product pattern to find the product $( 7 x + 2 ) ( 7 x - 2 )$ .

Find the difference $- 2 - \left( - 6 u ^ { 2 } - 8 \right)$ .