Question 1

Write the number in standard notation. $7.5 \times 10 ^ { - 6 }$

Accepted Answer

0.0000075

Question 2

The __________ of a polynomial is the same as the highest degree of any term of the polynomial.

Accepted Answer

degree

Question 3

The length of a rectangular garden is three more than twice the width. The area is 90square feet. Find the width. w = ________ feet

Accepted Answer

6

Question 4

Perform the indicated operation: $\left( 7 x ^ { 2 } - 5 x + 4 \right) - \left( - 4 x + 5 x ^ { 2 } - 1 \right)$

Accepted Answer

A)  $11 x ^ { 2 } - 10 x + 5$ 
B)  $12 x ^ { 2 } - x + 3$ 
C)  $2 x ^ { 4 } - x ^ { 2 } + 5$ 
D)  $2 x ^ { 2 } - x + 5$ 
A)  $11 x ^ { 2 } - 10 x + 5$ 
B)  $12 x ^ { 2 } - x + 3$ 
C)  $2 x ^ { 4 } - x ^ { 2 } + 5$ 
D)  $2 x ^ { 2 } - x + 5$

Question 5

Write the number in scientific notation. $2000 \times 10 ^ { - 6 }$  $\times 10 ^ { - }$

Accepted Answer

The answer of Write the number in scientific notation. \(2000...

Question 6

Factor the expression completely. $81 x ^ { 2 } - 18 x + 1 - 4 y ^ { 2 }$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(81 x ^...

Question 7

Factor the expression completely. If the expression is prime, so indicate. $x ^ { 2 } - y ^ { 2 } - 2 y - 1$

Accepted Answer

A)  $( x - y + 1 ) ( x - y - 1 )$ 
B)  $( x + y - 1 ) ( x - y + 1 )$ 
C)  $( x + y + 1 ) ( x + y - 1 )$ 
D)  $( x + y + 1 ) ( x - y - 1 )$ 
E)  prime 
A)  $( x - y + 1 ) ( x - y - 1 )$ 
B)  $( x + y - 1 ) ( x - y + 1 )$ 
C)  $( x + y + 1 ) ( x + y - 1 )$ 
D)  $( x + y + 1 ) ( x - y - 1 )$ 
E)  prime

Question 8

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 5 } } { b ^ { 2 } } \right) ^ { - 4 }$

Accepted Answer

The answer of Simplify the expression. Assume that variables represent...

Question 9

The mass of the Earth s oceans is only about $\frac { 1 } { 4400 }$ that of the Earth. If the mass of the Earth is $6.402 \times 10 ^ { 21 }$ tons, find the mass of the oceans.

Accepted Answer

A)  $2.81688 \times 10 ^ { 22 }$ tons 
B)  $2.81688 \times 10 ^ { 21 }$ tons 
C)  $1.455 \times 10 ^ { 18 }$ tons 
D)  $1.455 \times 10 ^ { 19 }$ tons 
E)  $1.455 \times 10 ^ { 20 }$ tons 
A)  $2.81688 \times 10 ^ { 22 }$ tons 
B)  $2.81688 \times 10 ^ { 21 }$ tons 
C)  $1.455 \times 10 ^ { 18 }$ tons 
D)  $1.455 \times 10 ^ { 19 }$ tons 
E)  $1.455 \times 10 ^ { 20 }$ tons

Question 10

A __________ is a polynomial with one term. A __________ is a polynomial with two terms. A __________ is a polynomial with three terms.

Accepted Answer

A)  monomial: one term trinomial: two terms binomial: three terms 
B)  trinomial: one term binomial: two terms monomial: three terms 
C)  trinomial: one term monomial: two terms binomial: three terms 
D)  monomial: one term binomial: two terms trinomial: three terms 
E)  binomial: one term monomial: two terms trinomial: three terms 
A)  monomial: one term trinomial: two terms binomial: three terms 
B)  trinomial: one term binomial: two terms monomial: three terms 
C)  trinomial: one term monomial: two terms binomial: three terms 
D)  monomial: one term binomial: two terms trinomial: three terms 
E)  binomial: one term monomial: two terms trinomial: three terms

Question 11

Perform the indicated operation: $4 b ^ { 2 } ( 3 b - 5 ) ( 5 b + 8 )$

Accepted Answer

A)  $120 b ^ { 6 } - 8 b ^ { 5 } - 320 b ^ { 4 }$ 
B)  $60 b ^ { 4 } - 4 b ^ { 3 } - 160 b ^ { 2 }$ 
C)  $60 b ^ { 4 } - 160 b ^ { 2 }$ 
D)  $60 b ^ { 4 } + 4 b ^ { 3 } - 160 b ^ { 2 }$ 
A)  $120 b ^ { 6 } - 8 b ^ { 5 } - 320 b ^ { 4 }$ 
B)  $60 b ^ { 4 } - 4 b ^ { 3 } - 160 b ^ { 2 }$ 
C)  $60 b ^ { 4 } - 160 b ^ { 2 }$ 
D)  $60 b ^ { 4 } + 4 b ^ { 3 } - 160 b ^ { 2 }$

Question 12

Evaluate: $\left( \frac { 4 } { 5 } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { 75 } { 48 }$ 
B)  $\frac { 64 } { 125 }$ 
C)  $- \frac { 64 } { 125 }$ 
D)  $\frac { 125 } { 64 }$ 
A)  $\frac { 75 } { 48 }$ 
B)  $\frac { 64 } { 125 }$ 
C)  $- \frac { 64 } { 125 }$ 
D)  $\frac { 125 } { 64 }$

Question 13

Simplify the expression. Write the answer using positive exponents. $- \frac { 6 t ^ { - 11 } t ^ { - 2 } } { t ^ { - 13 } }$

Accepted Answer

The answer of Simplify the expression. Write the answer using...

Question 14

Solve the equation. $68 a ^ { 2 } + 3 a - 5 = 0$ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(68 a ^ {...

Question 15

Subtract. $\left( 3 x ^ { 2 } y ^ { 3 } + 7 x y + 7 y ^ { 2 } \right) - \left( - 5 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)$

Accepted Answer

A)  $- 8 x ^ { 2 } y ^ { 3 } + 9 x y - 2 y ^ { 2 } + y$ 
B)  $8 x ^ { 2 } y ^ { 3 } + 9 x y + 7 y ^ { 2 } - y$ 
C)  $8 x ^ { 2 } y ^ { 3 } + 9 x y + 2 y ^ { 2 } - y$ 
D)  $8 x ^ { 2 } y ^ { 3 } - 9 x y + 5 y ^ { 2 } + y$ 
E)  $- 8 x ^ { 2 } y ^ { 3 } + 9 x y + 2 y ^ { 2 } - y$ 
A)  $- 8 x ^ { 2 } y ^ { 3 } + 9 x y - 2 y ^ { 2 } + y$ 
B)  $8 x ^ { 2 } y ^ { 3 } + 9 x y + 7 y ^ { 2 } - y$ 
C)  $8 x ^ { 2 } y ^ { 3 } + 9 x y + 2 y ^ { 2 } - y$ 
D)  $8 x ^ { 2 } y ^ { 3 } - 9 x y + 5 y ^ { 2 } + y$ 
E)  $- 8 x ^ { 2 } y ^ { 3 } + 9 x y + 2 y ^ { 2 } - y$

Question 16

Factor the expression completely. If the expression is prime, so indicate. $3 ( a - b ) ^ { 2 } + 5 ( a - b ) + 2$

Accepted Answer

A)  $( 3 a - b + 3 ) ( a - b + 1 )$ 
B)  $( 3 a - 3 b - 2 ) ( a - b - 1 )$ 
C)  $( 3 a - 3 b + 2 ) ( a - b + 1 )$ 
D)  $( 3 a - b - 3 ) ( a - b - 1 )$ 
E)  prime 
A)  $( 3 a - b + 3 ) ( a - b + 1 )$ 
B)  $( 3 a - 3 b - 2 ) ( a - b - 1 )$ 
C)  $( 3 a - 3 b + 2 ) ( a - b + 1 )$ 
D)  $( 3 a - b - 3 ) ( a - b - 1 )$ 
E)  prime

Question 17

Factor the expression completely. $9 c ^ { 2 } g ^ { 2 } + h ^ { 2 }$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(9 c ^...

Question 18

Determine what type of exponent must be used when writing real numbers between 0 and 1 using scientific notation.

Accepted Answer

A)  negative integer 
B)  positive integer 
C)  0 
A)  negative integer 
B)  positive integer 
C)  0

Question 19

Solve the equation. $z ^ { 2 } + 8 z + 12 = 0$

Accepted Answer

A)  $z = - 2 , z = - 6$ 
B)  $z = - 5 , z = - 8$ 
C)  $z = - 4 , z = - 5$ 
D)  $z = 2 , z = 6$ 
E)  $z = - 7 , z = 4$ 
A)  $z = - 2 , z = - 6$ 
B)  $z = - 5 , z = - 8$ 
C)  $z = - 4 , z = - 5$ 
D)  $z = 2 , z = 6$ 
E)  $z = - 7 , z = 4$

Question 20

Let $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2$ For what value(s) of x is $f ( x ) = 2$ ?

Accepted Answer

A)  $x = 1 , x = 3$ 
B)  $x = 4 , x = 1 , x = 5$ 
C)  $x = 2 , x = 1 , x = 1$ 
D)  $x = 0 , x = 2$ 
E)  $x = 0 , x = 1 , x = 2$ 
A)  $x = 1 , x = 3$ 
B)  $x = 4 , x = 1 , x = 5$ 
C)  $x = 2 , x = 1 , x = 1$ 
D)  $x = 0 , x = 2$ 
E)  $x = 0 , x = 1 , x = 2$

Write the number in standard notation. $7.5 \times 10 ^ { - 6 }$

The __________ of a polynomial is the same as the highest degree of any term of the polynomial.

The length of a rectangular garden is three more than twice the width. The area is 90square feet. Find the width. w = ________ feet

Perform the indicated operation: $\left( 7 x ^ { 2 } - 5 x + 4 \right) - \left( - 4 x + 5 x ^ { 2 } - 1 \right)$

Write the number in scientific notation. $2000 \times 10 ^ { - 6 }$ $Write the number in scientific notation. 2000 \times 10 ^ { - 6 } \times 10 ^ { - }$ $\times 10 ^ { - }$

Factor the expression completely. $81 x ^ { 2 } - 18 x + 1 - 4 y ^ { 2 }$ If the expression is prime, so indicate.

Factor the expression completely. If the expression is prime, so indicate. $x ^ { 2 } - y ^ { 2 } - 2 y - 1$

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 5 } } { b ^ { 2 } } \right) ^ { - 4 }$

The mass of the Earth s oceans is only about $\frac { 1 } { 4400 }$ that of the Earth. If the mass of the Earth is $6.402 \times 10 ^ { 21 }$ tons, find the mass of the oceans.

A is a polynomial with one term. A is a polynomial with two terms. A __ is a polynomial with three terms.

Perform the indicated operation: $4 b ^ { 2 } ( 3 b - 5 ) ( 5 b + 8 )$

Evaluate: $\left( \frac { 4 } { 5 } \right) ^ { - 3 }$

Simplify the expression. Write the answer using positive exponents. $- \frac { 6 t ^ { - 11 } t ^ { - 2 } } { t ^ { - 13 } }$

Solve the equation. $68 a ^ { 2 } + 3 a - 5 = 0$ If there is more than one solution, separate your answers with commas.

Subtract. $\left( 3 x ^ { 2 } y ^ { 3 } + 7 x y + 7 y ^ { 2 } \right) - \left( - 5 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)$

Factor the expression completely. If the expression is prime, so indicate. $3 ( a - b ) ^ { 2 } + 5 ( a - b ) + 2$

Factor the expression completely. $9 c ^ { 2 } g ^ { 2 } + h ^ { 2 }$ If the expression is prime, so indicate.

Determine what type of exponent must be used when writing real numbers between 0 and 1 using scientific notation.

Solve the equation. $z ^ { 2 } + 8 z + 12 = 0$

Let $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2$ For what value(s) of x is $f ( x ) = 2$ ?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

Write the number in standard notation. 7.5×10−67.5 \times 10 ^ { - 6 }7.5×10−6

The __________ of a polynomial is the same as the highest degree of any term of the polynomial.

The length of a rectangular garden is three more than twice the width. The area is 90square feet. Find the width. w = ________ feet

Perform the indicated operation: (7x2−5x+4)−(−4x+5x2−1)\left( 7 x ^ { 2 } - 5 x + 4 \right) - \left( - 4 x + 5 x ^ { 2 } - 1 \right)(7x2−5x+4)−(−4x+5x2−1)

Write the number in scientific notation. 2000×10−62000 \times 10 ^ { - 6 }2000×10−6 ×10−\times 10 ^ { - }×10−

Factor the expression completely. 81x2−18x+1−4y281 x ^ { 2 } - 18 x + 1 - 4 y ^ { 2 }81x2−18x+1−4y2 If the expression is prime, so indicate.

Factor the expression completely. If the expression is prime, so indicate. x2−y2−2y−1x ^ { 2 } - y ^ { 2 } - 2 y - 1x2−y2−2y−1

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. (a5b2)−4\left( \frac { a ^ { 5 } } { b ^ { 2 } } \right) ^ { - 4 }(b2a5​)−4

The mass of the Earth s oceans is only about 14400\frac { 1 } { 4400 }44001​ that of the Earth. If the mass of the Earth is 6.402×10216.402 \times 10 ^ { 21 }6.402×1021 tons, find the mass of the oceans.

A __________ is a polynomial with one term. A __________ is a polynomial with two terms. A __________ is a polynomial with three terms.

Perform the indicated operation: 4b2(3b−5)(5b+8)4 b ^ { 2 } ( 3 b - 5 ) ( 5 b + 8 )4b2(3b−5)(5b+8)

Evaluate: (45)−3\left( \frac { 4 } { 5 } \right) ^ { - 3 }(54​)−3

Simplify the expression. Write the answer using positive exponents. −6t−11t−2t−13- \frac { 6 t ^ { - 11 } t ^ { - 2 } } { t ^ { - 13 } }−t−136t−11t−2​

Solve the equation. 68a2+3a−5=068 a ^ { 2 } + 3 a - 5 = 068a2+3a−5=0 If there is more than one solution, separate your answers with commas.

Subtract. (3x2y3+7xy+7y2)−(−5x2y3−2xy+5y2+y)\left( 3 x ^ { 2 } y ^ { 3 } + 7 x y + 7 y ^ { 2 } \right) - \left( - 5 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)(3x2y3+7xy+7y2)−(−5x2y3−2xy+5y2+y)

Factor the expression completely. If the expression is prime, so indicate. 3(a−b)2+5(a−b)+23 ( a - b ) ^ { 2 } + 5 ( a - b ) + 23(a−b)2+5(a−b)+2

Factor the expression completely. 9c2g2+h29 c ^ { 2 } g ^ { 2 } + h ^ { 2 }9c2g2+h2 If the expression is prime, so indicate.

Determine what type of exponent must be used when writing real numbers between 0 and 1 using scientific notation.

Solve the equation. z2+8z+12=0z ^ { 2 } + 8 z + 12 = 0z2+8z+12=0

Let f(x)=x3−3x2+2x+2f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2f(x)=x3−3x2+2x+2 For what value(s) of x is f(x)=2f ( x ) = 2f(x)=2 ?

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Write the number in standard notation. $7.5 \times 10 ^ { - 6 }$

Perform the indicated operation: $\left( 7 x ^ { 2 } - 5 x + 4 \right) - \left( - 4 x + 5 x ^ { 2 } - 1 \right)$

Write the number in scientific notation. $2000 \times 10 ^ { - 6 }$ $Write the number in scientific notation. 2000 \times 10 ^ { - 6 } \times 10 ^ { - }$ $\times 10 ^ { - }$

Factor the expression completely. $81 x ^ { 2 } - 18 x + 1 - 4 y ^ { 2 }$ If the expression is prime, so indicate.

Factor the expression completely. If the expression is prime, so indicate. $x ^ { 2 } - y ^ { 2 } - 2 y - 1$

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 5 } } { b ^ { 2 } } \right) ^ { - 4 }$

The mass of the Earth s oceans is only about $\frac { 1 } { 4400 }$ that of the Earth. If the mass of the Earth is $6.402 \times 10 ^ { 21 }$ tons, find the mass of the oceans.

A is a polynomial with one term. A is a polynomial with two terms. A __ is a polynomial with three terms.

Perform the indicated operation: $4 b ^ { 2 } ( 3 b - 5 ) ( 5 b + 8 )$

Evaluate: $\left( \frac { 4 } { 5 } \right) ^ { - 3 }$

Simplify the expression. Write the answer using positive exponents. $- \frac { 6 t ^ { - 11 } t ^ { - 2 } } { t ^ { - 13 } }$

Solve the equation. $68 a ^ { 2 } + 3 a - 5 = 0$ If there is more than one solution, separate your answers with commas.

Subtract. $\left( 3 x ^ { 2 } y ^ { 3 } + 7 x y + 7 y ^ { 2 } \right) - \left( - 5 x ^ { 2 } y ^ { 3 } - 2 x y + 5 y ^ { 2 } + y \right)$

Factor the expression completely. If the expression is prime, so indicate. $3 ( a - b ) ^ { 2 } + 5 ( a - b ) + 2$

Factor the expression completely. $9 c ^ { 2 } g ^ { 2 } + h ^ { 2 }$ If the expression is prime, so indicate.

Solve the equation. $z ^ { 2 } + 8 z + 12 = 0$

Let $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2$ For what value(s) of x is $f ( x ) = 2$ ?