Question 1

Use a special product pattern to find the product $( 7 x + 1 ) ^ { 2 }$.

Accepted Answer

A)  $49 x ^ { 2 } - 1$ 
B)  $49 x ^ { 2 } + 16 x + 1$ 
C)  $49 x ^ { 2 } + 1$ 
D)  $49 x ^ { 2 } + 7 x + 1$ 
E)  $49 x ^ { 2 } + 14 x + 1$ 
A)  $49 x ^ { 2 } - 1$ 
B)  $49 x ^ { 2 } + 16 x + 1$ 
C)  $49 x ^ { 2 } + 1$ 
D)  $49 x ^ { 2 } + 7 x + 1$ 
E)  $49 x ^ { 2 } + 14 x + 1$

Question 2

A closed rectangular box has dimensions of length n inches, width n+6 inches, and height n+2 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box.

Accepted Answer

A)  $A ( n ) = n ^ { 2 } - 2 n + 12$ 
B)  $A ( n ) = - n ^ { 2 } + 6 n + 12$ 
C)  $A ( n ) = n ^ { 2 } - 4 n + 12$ 
D)  $A ( n ) = n ^ { 2 } + 4 n + 12$ 
E)  $A ( n ) = n ^ { 2 } + 8 n + 12$ 
A)  $A ( n ) = n ^ { 2 } - 2 n + 12$ 
B)  $A ( n ) = - n ^ { 2 } + 6 n + 12$ 
C)  $A ( n ) = n ^ { 2 } - 4 n + 12$ 
D)  $A ( n ) = n ^ { 2 } + 4 n + 12$ 
E)  $A ( n ) = n ^ { 2 } + 8 n + 12$

Question 3

Write the number 154 as a product of prime factors.

Accepted Answer

A)  2.7.14 
B)  7.11 
C)  2.7.11 
D)  11.14 
E)  7.22 
A)  2.7.14 
B)  7.11 
C)  2.7.11 
D)  11.14 
E)  7.22

Question 4

Factor the trinomial below. $x ^ { 2 } - x - 6$

Accepted Answer

A)  $( x + 3 ) ( x - 2 )$ 
B)  $( x - 3 ) ( x - 2 )$ 
C)  $( x + 3 ) ( x + 2 )$ 
D)  $( x - 3 ) ( x + 2 )$ 
E)  $( x - 3 ) ( x + 3 )$ 
A)  $( x + 3 ) ( x - 2 )$ 
B)  $( x - 3 ) ( x - 2 )$ 
C)  $( x + 3 ) ( x + 2 )$ 
D)  $( x - 3 ) ( x + 2 )$ 
E)  $( x - 3 ) ( x + 3 )$

Question 5

Perform the indicated operations and simplify. $\left( 8 x ^ { 2 } + 5 x + 6 \right) - \left[ \left( - 6 x ^ { 3 } + 3 x ^ { 2 } - 19 \right) + ( - 7 x + 11 ) \right]$

Accepted Answer

A)  $- 6 x ^ { 3 } + 11 x ^ { 2 } + 12 x + 14$ 
B)  $6 x ^ { 3 } + 5 x ^ { 2 } - 2 x - 2$ 
C)  $6 x ^ { 3 } + 11 x ^ { 2 } - 2 x - 2$ 
D)  $6 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 14$ 
E)  $- 6 x ^ { 3 } + 5 x ^ { 2 } - 2 x - 2$ 
A)  $- 6 x ^ { 3 } + 11 x ^ { 2 } + 12 x + 14$ 
B)  $6 x ^ { 3 } + 5 x ^ { 2 } - 2 x - 2$ 
C)  $6 x ^ { 3 } + 11 x ^ { 2 } - 2 x - 2$ 
D)  $6 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 14$ 
E)  $- 6 x ^ { 3 } + 5 x ^ { 2 } - 2 x - 2$

Question 6

Multiply $( 3 x + 5 ) \left( x ^ { 2 } + 9 x - 2 \right)$ and simplify.

Accepted Answer

A)  $3 x ^ { 3 } + 32 x ^ { 2 } + 9 x - 2$ 
B)  $3 x ^ { 3 } + 5 x ^ { 2 } + 45 x - 2$ 
C)  $3 x ^ { 3 } + 45 x ^ { 2 } - 2$ 
D)  $3 x ^ { 3 } + 5 x ^ { 2 } + 39 x - 10$ 
E)  $3 x ^ { 3 } + 32 x ^ { 2 } + 39 x - 10$ 
A)  $3 x ^ { 3 } + 32 x ^ { 2 } + 9 x - 2$ 
B)  $3 x ^ { 3 } + 5 x ^ { 2 } + 45 x - 2$ 
C)  $3 x ^ { 3 } + 45 x ^ { 2 } - 2$ 
D)  $3 x ^ { 3 } + 5 x ^ { 2 } + 39 x - 10$ 
E)  $3 x ^ { 3 } + 32 x ^ { 2 } + 39 x - 10$

Question 7

Which of the following polynomials is a binomial of degree 3?

Accepted Answer

A)  $3 x ^ { 3 } + 9 x$ 
B)  $3 x ^ { 3 } + 9 x ^ { 2 } + 6 x + 2$ 
C)  $3 x ^ { 2 } + 9 x + 6$ 
D)  $3 x ^ { 2 } + 3 x$ 
E)  $3 x ^ { 3 } + 9 x + 6$ 
A)  $3 x ^ { 3 } + 9 x$ 
B)  $3 x ^ { 3 } + 9 x ^ { 2 } + 6 x + 2$ 
C)  $3 x ^ { 2 } + 9 x + 6$ 
D)  $3 x ^ { 2 } + 3 x$ 
E)  $3 x ^ { 3 } + 9 x + 6$

Question 8

Use a special product pattern to find the product $( x - 8 ) ^ { 2 }$ .

Accepted Answer

A)  $x ^ { 2 } - 16 x + 64$ 
B)  $x ^ { 2 } - 64$ 
C)  $x ^ { 2 } + 64$ 
D)  $x ^ { 2 } + 16 x + 64$ 
E)  $x ^ { 2 } - 8 x + 64$ 
A)  $x ^ { 2 } - 16 x + 64$ 
B)  $x ^ { 2 } - 64$ 
C)  $x ^ { 2 } + 64$ 
D)  $x ^ { 2 } + 16 x + 64$ 
E)  $x ^ { 2 } - 8 x + 64$

Question 9

Use the rules of exponents to simplify the expression below. $\left[ \frac { \left( 2 x ^ { 2 } \right) ( 2 x ) ^ { 2 } } { \left( - 2 x ^ { 2 } \right) ( 2 x ) } \right] ^ { 2 }$

Accepted Answer

A)  $4 x ^ { 2 }$ 
B)  $- 6 x ^ { 5 }$ 
C)  $3 x ^ { 2 }$ 
D)  $14 x ^ { 7 }$ 
E)  $5 x ^ { 6 }$ 
A)  $4 x ^ { 2 }$ 
B)  $- 6 x ^ { 5 }$ 
C)  $3 x ^ { 2 }$ 
D)  $14 x ^ { 7 }$ 
E)  $5 x ^ { 6 }$

Question 10

Solve the equation below by factoring. $$( t + 5 ) ^ { 2 } = 36$$

Accepted Answer

A)  $t = - 1$ and $t = 1$ 
B)  $t = - 11$ and $t = 1$ 
C)  $t = - 1$ and $t = 11$ 
D)  $t = 1$ and $t = 11$ 
E)  $t = - 11$ and $t = - 1$ 
A)  $t = - 1$ and $t = 1$ 
B)  $t = - 11$ and $t = 1$ 
C)  $t = - 1$ and $t = 11$ 
D)  $t = 1$ and $t = 11$ 
E)  $t = - 11$ and $t = - 1$

Question 11

Write the number $0.00161$ in scientific notation.

Accepted Answer

A)  $1.61 \times 10 ^ { - 4 }$ 
B)  $1.61 \times 10 ^ { - 2 }$ 
C)  $1.61 \times 10 ^ { - 3 }$ 
D)  $1.61 \times 10 ^ { 3 }$ 
E)  $1.61 \times 10 ^ { 2 }$ 
A)  $1.61 \times 10 ^ { - 4 }$ 
B)  $1.61 \times 10 ^ { - 2 }$ 
C)  $1.61 \times 10 ^ { - 3 }$ 
D)  $1.61 \times 10 ^ { 3 }$ 
E)  $1.61 \times 10 ^ { 2 }$

Question 12

Solve the equation below by factoring. $9 z ^ { 2 } - 48 z + 70 = 6$

Accepted Answer

A)  $- 24,0$ 
B)  $- \frac { 8 } { 3 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  $24,0$ 
E)  $\pm \frac { 8 } { 3 }$ 
A)  $- 24,0$ 
B)  $- \frac { 8 } { 3 }$ 
C)  $\frac { 8 } { 3 }$ 
D)  $24,0$ 
E)  $\pm \frac { 8 } { 3 }$

Question 13

Rewrite the expression $3 x ^ { - 4 }$ using only positive exponents. Assume that x is not zero.

Accepted Answer

A)  $\frac { 1 } { 81 x ^ { 4 } }$ 
B)  $\frac { 3 } { x ^ { 4 } }$ 
C)  $\frac { 1 } { 3 x ^ { 4 } }$ 
D)  $- \frac { 3 } { x ^ { 4 } }$ 
E)  $- \frac { 1 } { 81 x ^ { 4 } }$ 
A)  $\frac { 1 } { 81 x ^ { 4 } }$ 
B)  $\frac { 3 } { x ^ { 4 } }$ 
C)  $\frac { 1 } { 3 x ^ { 4 } }$ 
D)  $- \frac { 3 } { x ^ { 4 } }$ 
E)  $- \frac { 1 } { 81 x ^ { 4 } }$

Question 14

Evaluate the expression below without a calculator. $\frac { 68000 } { 0.00001 }$

Accepted Answer

A)  $6,800,000$ 
B)  $68,000,000$ 
C)  $68,000,000,000$ 
D)  $6,800,000,000$ 
E)  $680,000,000,000$ 
A)  $6,800,000$ 
B)  $68,000,000$ 
C)  $68,000,000,000$ 
D)  $6,800,000,000$ 
E)  $680,000,000,000$

Question 15

Use a vertical format to find the product of the two polynomials. $\left( 3 x ^ { 2 } - 4 x - 4 \right) \left( 3 x ^ { 2 } - 4 x - 1 \right)$

Accepted Answer

A)  $9 x ^ { 5 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x + 4$ 
B)  $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x + 4$ 
C)  $9 x ^ { 4 } - 24 x ^ { 3 } + 20 x + 4$ 
D)  $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 4$ 
E)  $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x$ 
A)  $9 x ^ { 5 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x + 4$ 
B)  $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x + 4$ 
C)  $9 x ^ { 4 } - 24 x ^ { 3 } + 20 x + 4$ 
D)  $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 4$ 
E)  $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x$

Question 16

Multiply: $- 9 x \left( 2 x ^ { 6 } - 5 x ^ { 3 } + 8 \right)$

Accepted Answer

A)  $- 18 x ^ { 7 } + 45 x ^ { 4 } - 72 x$ 
B)  $- 18 x ^ { 7 } + 5 x ^ { 3 } - 8 x$ 
C)  $- 18 x ^ { 7 } - 45 x ^ { 4 } + 72 x$ 
D)  $- 18 x ^ { 7 } + 45 x ^ { 4 } + 72 x$ 
E)  $- 18 x ^ { 7 } - 5 x ^ { 3 } + 8 x$ 
A)  $- 18 x ^ { 7 } + 45 x ^ { 4 } - 72 x$ 
B)  $- 18 x ^ { 7 } + 5 x ^ { 3 } - 8 x$ 
C)  $- 18 x ^ { 7 } - 45 x ^ { 4 } + 72 x$ 
D)  $- 18 x ^ { 7 } + 45 x ^ { 4 } + 72 x$ 
E)  $- 18 x ^ { 7 } - 5 x ^ { 3 } + 8 x$

Question 17

An object is thrown upwards from the top of a building, which is 1296 feet tall. The initial velocity is 3 feet per second. Use the position function below to find the height of the object when t=2 seconds. $s = - 16 t ^ { 2 } + 3 t + 1296$

Accepted Answer

A) 58 feet 
B) 1354 feet 
C) 1226 feet 
D) 1238 feet 
E) 1366 feet 
A) 58 feet 
B) 1354 feet 
C) 1226 feet 
D) 1238 feet 
E) 1366 feet

Question 18

Perform the indicated operations and simplify. $\left( 7 x ^ { 4 } + 3 x ^ { 2 } \right) + 3 \left( - 5 x ^ { 4 } - 5 x ^ { 2 } \right)$

Accepted Answer

A)  $- 8 x ^ { 4 } - 12 x ^ { 2 }$ 
B)  $22 x ^ { 4 } + 18 x ^ { 2 }$ 
C)  $22 x ^ { 4 } - 2 x ^ { 2 }$ 
D)  $22 x ^ { 4 } - 12 x ^ { 2 }$ 
E)  $- 8 x ^ { 4 } - 2 x ^ { 2 }$ 
A)  $- 8 x ^ { 4 } - 12 x ^ { 2 }$ 
B)  $22 x ^ { 4 } + 18 x ^ { 2 }$ 
C)  $22 x ^ { 4 } - 2 x ^ { 2 }$ 
D)  $22 x ^ { 4 } - 12 x ^ { 2 }$ 
E)  $- 8 x ^ { 4 } - 2 x ^ { 2 }$

Question 19

Write the number $5.92 \times 10 ^ { - 3 }$ in decimal notation.

Accepted Answer

A)  $59,200$ 
B)  59.2 
C)  $0.00592$ 
D)  $592,000$ 
E)  0.592 
A)  $59,200$ 
B)  59.2 
C)  $0.00592$ 
D)  $592,000$ 
E)  0.592

Question 20

Use the area model to write the simplified expression for the total area below.

Accepted Answer

A)  $x ^ { 2 } + 3 x$ 
B)  $x ^ { 2 } + 9$ 
C)  $x ^ { 2 } + 9 x$ 
D)  $x ^ { 2 } + 6 x + 9$ 
E)  $x ^ { 2 } + 3 x + 9$ 
A)  $x ^ { 2 } + 3 x$ 
B)  $x ^ { 2 } + 9$ 
C)  $x ^ { 2 } + 9 x$ 
D)  $x ^ { 2 } + 6 x + 9$ 
E)  $x ^ { 2 } + 3 x + 9$

Use a special product pattern to find the product $( 7 x + 1 ) ^ { 2 }$ .

A closed rectangular box has dimensions of length n inches, width n+6 inches, and height n+2 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box.

Write the number 154 as a product of prime factors.

Factor the trinomial below. $x ^ { 2 } - x - 6$

Perform the indicated operations and simplify. $\left( 8 x ^ { 2 } + 5 x + 6 \right) - \left[ \left( - 6 x ^ { 3 } + 3 x ^ { 2 } - 19 \right) + ( - 7 x + 11 ) \right]$

Multiply $( 3 x + 5 ) \left( x ^ { 2 } + 9 x - 2 \right)$ and simplify.

Which of the following polynomials is a binomial of degree 3?

Use a special product pattern to find the product $( x - 8 ) ^ { 2 }$ .

Use the rules of exponents to simplify the expression below. $\left[ \frac { \left( 2 x ^ { 2 } \right) ( 2 x ) ^ { 2 } } { \left( - 2 x ^ { 2 } \right) ( 2 x ) } \right] ^ { 2 }$

Solve the equation below by factoring. $( t + 5 ) ^ { 2 } = 36$

Write the number $0.00161$ in scientific notation.

Solve the equation below by factoring. $9 z ^ { 2 } - 48 z + 70 = 6$

Rewrite the expression $3 x ^ { - 4 }$ using only positive exponents. Assume that x is not zero.

Evaluate the expression below without a calculator. $\frac { 68000 } { 0.00001 }$

Use a vertical format to find the product of the two polynomials. $\left( 3 x ^ { 2 } - 4 x - 4 \right) \left( 3 x ^ { 2 } - 4 x - 1 \right)$

Multiply: $- 9 x \left( 2 x ^ { 6 } - 5 x ^ { 3 } + 8 \right)$

An object is thrown upwards from the top of a building, which is 1296 feet tall. The initial velocity is 3 feet per second. Use the position function below to find the height of the object when t=2 seconds. $s = - 16 t ^ { 2 } + 3 t + 1296$

Perform the indicated operations and simplify. $\left( 7 x ^ { 4 } + 3 x ^ { 2 } \right) + 3 \left( - 5 x ^ { 4 } - 5 x ^ { 2 } \right)$

Write the number $5.92 \times 10 ^ { - 3 }$ in decimal notation.

Use the area model to write the simplified expression for the total area below.

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

Exam 5: Polynomials and Factoring

Use a special product pattern to find the product (7x+1)2( 7 x + 1 ) ^ { 2 }(7x+1)2 .

A closed rectangular box has dimensions of length n inches, width n+6 inches, and height n+2 inches. Write a polynomial function A(n)A ( n )A(n) for the area of the largest side of the box.

Write the number 154 as a product of prime factors.

Factor the trinomial below. x2−x−6x ^ { 2 } - x - 6x2−x−6

Perform the indicated operations and simplify. (8x2+5x+6)−[(−6x3+3x2−19)+(−7x+11)]\left( 8 x ^ { 2 } + 5 x + 6 \right) - \left[ \left( - 6 x ^ { 3 } + 3 x ^ { 2 } - 19 \right) + ( - 7 x + 11 ) \right](8x2+5x+6)−[(−6x3+3x2−19)+(−7x+11)]

Multiply (3x+5)(x2+9x−2)( 3 x + 5 ) \left( x ^ { 2 } + 9 x - 2 \right)(3x+5)(x2+9x−2) and simplify.

Which of the following polynomials is a binomial of degree 3?

Use a special product pattern to find the product (x−8)2( x - 8 ) ^ { 2 }(x−8)2 .

Use the rules of exponents to simplify the expression below. [(2x2)(2x)2(−2x2)(2x)]2\left[ \frac { \left( 2 x ^ { 2 } \right) ( 2 x ) ^ { 2 } } { \left( - 2 x ^ { 2 } \right) ( 2 x ) } \right] ^ { 2 }[(−2x2)(2x)(2x2)(2x)2​]2

Solve the equation below by factoring. (t+5)2=36( t + 5 ) ^ { 2 } = 36(t+5)2=36

Write the number 0.001610.001610.00161 in scientific notation.

Solve the equation below by factoring. 9z2−48z+70=69 z ^ { 2 } - 48 z + 70 = 69z2−48z+70=6

Rewrite the expression 3x−43 x ^ { - 4 }3x−4 using only positive exponents. Assume that x is not zero.

Evaluate the expression below without a calculator. 680000.00001\frac { 68000 } { 0.00001 }0.0000168000​

Use a vertical format to find the product of the two polynomials. (3x2−4x−4)(3x2−4x−1)\left( 3 x ^ { 2 } - 4 x - 4 \right) \left( 3 x ^ { 2 } - 4 x - 1 \right)(3x2−4x−4)(3x2−4x−1)

Multiply: −9x(2x6−5x3+8)- 9 x \left( 2 x ^ { 6 } - 5 x ^ { 3 } + 8 \right)−9x(2x6−5x3+8)

An object is thrown upwards from the top of a building, which is 1296 feet tall. The initial velocity is 3 feet per second. Use the position function below to find the height of the object when t=2 seconds. s=−16t2+3t+1296s = - 16 t ^ { 2 } + 3 t + 1296s=−16t2+3t+1296

Perform the indicated operations and simplify. (7x4+3x2)+3(−5x4−5x2)\left( 7 x ^ { 4 } + 3 x ^ { 2 } \right) + 3 \left( - 5 x ^ { 4 } - 5 x ^ { 2 } \right)(7x4+3x2)+3(−5x4−5x2)

Write the number 5.92×10−35.92 \times 10 ^ { - 3 }5.92×10−3 in decimal notation.

Use the area model to write the simplified expression for the total area below.

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

Use a special product pattern to find the product $( 7 x + 1 ) ^ { 2 }$ .

A closed rectangular box has dimensions of length n inches, width n+6 inches, and height n+2 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box.

Factor the trinomial below. $x ^ { 2 } - x - 6$

Perform the indicated operations and simplify. $\left( 8 x ^ { 2 } + 5 x + 6 \right) - \left[ \left( - 6 x ^ { 3 } + 3 x ^ { 2 } - 19 \right) + ( - 7 x + 11 ) \right]$

Multiply $( 3 x + 5 ) \left( x ^ { 2 } + 9 x - 2 \right)$ and simplify.

Use a special product pattern to find the product $( x - 8 ) ^ { 2 }$ .

Use the rules of exponents to simplify the expression below. $\left[ \frac { \left( 2 x ^ { 2 } \right) ( 2 x ) ^ { 2 } } { \left( - 2 x ^ { 2 } \right) ( 2 x ) } \right] ^ { 2 }$

Solve the equation below by factoring. $( t + 5 ) ^ { 2 } = 36$

Write the number $0.00161$ in scientific notation.

Solve the equation below by factoring. $9 z ^ { 2 } - 48 z + 70 = 6$

Rewrite the expression $3 x ^ { - 4 }$ using only positive exponents. Assume that x is not zero.

Evaluate the expression below without a calculator. $\frac { 68000 } { 0.00001 }$

Use a vertical format to find the product of the two polynomials. $\left( 3 x ^ { 2 } - 4 x - 4 \right) \left( 3 x ^ { 2 } - 4 x - 1 \right)$

Multiply: $- 9 x \left( 2 x ^ { 6 } - 5 x ^ { 3 } + 8 \right)$

An object is thrown upwards from the top of a building, which is 1296 feet tall. The initial velocity is 3 feet per second. Use the position function below to find the height of the object when t=2 seconds. $s = - 16 t ^ { 2 } + 3 t + 1296$

Perform the indicated operations and simplify. $\left( 7 x ^ { 4 } + 3 x ^ { 2 } \right) + 3 \left( - 5 x ^ { 4 } - 5 x ^ { 2 } \right)$

Write the number $5.92 \times 10 ^ { - 3 }$ in decimal notation.