Question 1

Divide the polynomials by using an appropriate method. $$\left( s ^ { 4 } + 8 s ^ { 3 } + 2 s ^ { 2 } - 8 s - 5 \right) \div ( s + 1 )$$

Accepted Answer

A)  $s ^ { 3 } + 7 s ^ { 2 } - 5 s + \frac { - 3 s + 2 } { s + 1 }$ 
B)  $s ^ { 3 } + 7 s ^ { 2 } - 5 s - 3$ 
C)  $s ^ { 3 } + 9 s ^ { 2 } + 11 s + 3 - \frac { 2 } { s - 1 }$ 
D)  $s ^ { 3 } + 7 s ^ { 2 } - 5 s - 3 - \frac { 2 } { s + 1 }$ 
A)  $s ^ { 3 } + 7 s ^ { 2 } - 5 s + \frac { - 3 s + 2 } { s + 1 }$ 
B)  $s ^ { 3 } + 7 s ^ { 2 } - 5 s - 3$ 
C)  $s ^ { 3 } + 9 s ^ { 2 } + 11 s + 3 - \frac { 2 } { s - 1 }$ 
D)  $s ^ { 3 } + 7 s ^ { 2 } - 5 s - 3 - \frac { 2 } { s + 1 }$

Question 2

Translate from English form to algebraic form. The square of the difference of 2x + y and 8

Accepted Answer

A)  $( 2 x + y ) ^ { 2 } - 8 ^ { 2 }$ 
B)  $8 ^ { 2 } - ( 2 x + y ) ^ { 2 }$ 
C)  $[ ( 2 x + y ) - 8 ) ^ { 2 }$ 
D)  $( 2 x + y ) ^ { 2 } - 8$ 
A)  $( 2 x + y ) ^ { 2 } - 8 ^ { 2 }$ 
B)  $8 ^ { 2 } - ( 2 x + y ) ^ { 2 }$ 
C)  $[ ( 2 x + y ) - 8 ) ^ { 2 }$ 
D)  $( 2 x + y ) ^ { 2 } - 8$

Question 3

Simplify the expression. Write your answer with positive exponents only. $\frac { z ^ { 2 } y ^ { 6 } } { y ^ { - 6 } z ^ { 9 } }$

Accepted Answer

A)  $\frac { 1 } { z ^ { 7 } y ^ { 12 } }$ 
B)  $\frac { y ^ { 12 } } { z ^ { 7 } }$ 
C)  $\frac { 1 } { z ^ { 7 } }$ 
D)  $z ^ { 7 } y ^ { 6 }$ 
A)  $\frac { 1 } { z ^ { 7 } y ^ { 12 } }$ 
B)  $\frac { y ^ { 12 } } { z ^ { 7 } }$ 
C)  $\frac { 1 } { z ^ { 7 } }$ 
D)  $z ^ { 7 } y ^ { 6 }$

Question 4

Multiply the polynomials by using the distributive property. $$( - 7.3 n + 4.7 p ) ( - 4.6 n + 3.1 p )$$

Accepted Answer

A)  $- 11.9 n ^ { 2 } - 44.25 n p + 7.8 p ^ { 2 }$ 
B)  $33.58 n ^ { 2 } - 22.63 n - 21.62 p + 14.57 p ^ { 2 }$ 
C)  $33.58 n ^ { 2 } - 44.25 n p + 14.57 p ^ { 2 }$ 
D)  $33.58 n - 44.25 n p + 14.57 p$ 
A)  $- 11.9 n ^ { 2 } - 44.25 n p + 7.8 p ^ { 2 }$ 
B)  $33.58 n ^ { 2 } - 22.63 n - 21.62 p + 14.57 p ^ { 2 }$ 
C)  $33.58 n ^ { 2 } - 44.25 n p + 14.57 p ^ { 2 }$ 
D)  $33.58 n - 44.25 n p + 14.57 p$

Question 5

Multiply by using the special case products. $$\left( \frac { 2 } { 3 } w + 1 \right) ^ { 2 }$$

Accepted Answer

A)  $\frac { 4 } { 9 } w ^ { 2 } + \frac { 2 } { 3 } w + 1$ 
B)  $\frac { 4 } { 9 } w ^ { 2 } + \frac { 4 } { 3 } w + 1$ 
C)  $\frac { 4 } { 9 } w ^ { 2 } + 1$ 
D)  $\frac { 4 } { 9 } w ^ { 2 } - \frac { 2 } { 3 } w - 1$ 
A)  $\frac { 4 } { 9 } w ^ { 2 } + \frac { 2 } { 3 } w + 1$ 
B)  $\frac { 4 } { 9 } w ^ { 2 } + \frac { 4 } { 3 } w + 1$ 
C)  $\frac { 4 } { 9 } w ^ { 2 } + 1$ 
D)  $\frac { 4 } { 9 } w ^ { 2 } - \frac { 2 } { 3 } w - 1$

Question 6

Simplify the expression. Write your answer with positive exponents only. $\left( 2 x ^ { 6 } \right) ^ { 4 }$

Accepted Answer

A)  $2 x ^ { 10 }$ 
B)  $16 x ^ { 10 }$ 
C)  $2 x ^ { 24 }$ 
D)  $16 x ^ { 24 }$ 
A)  $2 x ^ { 10 }$ 
B)  $16 x ^ { 10 }$ 
C)  $2 x ^ { 24 }$ 
D)  $16 x ^ { 24 }$

Question 7

Write the number in scientific notation. 0.00000063

Accepted Answer

A)  $6.3 \times 10 ^ { 7 }$ 
B)  $63 \times 10 ^ { - 8 }$ 
C)  $0.63 \times 10 ^ { - 6 }$ 
D)  $6.3 \times 10 ^ { - 7 }$ 
A)  $6.3 \times 10 ^ { 7 }$ 
B)  $63 \times 10 ^ { - 8 }$ 
C)  $0.63 \times 10 ^ { - 6 }$ 
D)  $6.3 \times 10 ^ { - 7 }$

Question 8

Simplify the expression. Write your answer with positive exponents only. $y ^ { 8 } \cdot y ^ { 5 }$

Accepted Answer

A)  $y ^ { 3 }$ 
B)  $y ^ { 40 }$ 
C)  $y ^ { 26 }$ 
D)  $y ^ { 13 }$ 
A)  $y ^ { 3 }$ 
B)  $y ^ { 40 }$ 
C)  $y ^ { 26 }$ 
D)  $y ^ { 13 }$

Question 9

Simplify. $$\left( - \frac { 21 } { 16 } \right) ^ { 0 }$$

Accepted Answer

A)  $- \frac { 21 } { 16 }$ 
B)  $\frac { 1 } { 16 }$ 
C)  0 
D)  1 
A)  $- \frac { 21 } { 16 }$ 
B)  $\frac { 1 } { 16 }$ 
C)  0 
D)  1

Question 10

Subtract the polynomials and simplify. $$\left( - 3 r ^ { 2 } - 2 r - 4 \right) - \left( - 9 r ^ { 2 } + 7 r + 2 \right)$$

Accepted Answer

A)  $- 12 r ^ { 2 } + 5 r - 2$ 
B)  $6 r ^ { 2 } - 9 r - 6$ 
C)  $6 r ^ { 2 } - 2 r ^ { 2 } - 7 r - 6$ 
D)  $6 r ^ { 2 } + 5 r - 2$ 
A)  $- 12 r ^ { 2 } + 5 r - 2$ 
B)  $6 r ^ { 2 } - 9 r - 6$ 
C)  $6 r ^ { 2 } - 2 r ^ { 2 } - 7 r - 6$ 
D)  $6 r ^ { 2 } + 5 r - 2$

Question 11

Divide by using synthetic division. $$\left( s ^ { 2 } + 12 s + 27 \right) \div ( s + 3 )$$

Accepted Answer

A)  $s - 9 - \frac { 18 } { s + 3 }$ 
B)  $s - 9 + \frac { 18 } { s + 3 }$ 
C)  $s - 9$ 
D)  $s + 9$ 
A)  $s - 9 - \frac { 18 } { s + 3 }$ 
B)  $s - 9 + \frac { 18 } { s + 3 }$ 
C)  $s - 9$ 
D)  $s + 9$

Question 12

The following table represents the result of a synthetic division.

Use $x$ as the variable. Identify the dividend.

Accepted Answer

A)  $- 5$ 
B)  $9 x ^ { 2 } - 7 x + 4$ 
C)  $9 x ^ { 3 } + 2 x ^ { 2 } - 3 x - 1$ 
D)  $x + 1$ 
A)  $- 5$ 
B)  $9 x ^ { 2 } - 7 x + 4$ 
C)  $9 x ^ { 3 } + 2 x ^ { 2 } - 3 x - 1$ 
D)  $x + 1$

Question 13

A box is created from a square piece of cardboard with sides measuring s = 16 cm by cutting a square from each corner and folding up the sides. Let x represent the length of the sides of the squares Removed from each corner.
Find an expression representing the volume of the box.

Accepted Answer

A)  $V = 4 x ^ { 3 } - 64 x ^ { 2 } + 256 x$ 
B)  $V = x ^ { 3 } - 64 x ^ { 2 } + 1024 x$ 
C)  $V = x ^ { 3 } - 32 x ^ { 2 } + 256 x$ 
D)  $V = 16 x ^ { 2 } + 4 x ^ { 3 }$ 
A)  $V = 4 x ^ { 3 } - 64 x ^ { 2 } + 256 x$ 
B)  $V = x ^ { 3 } - 64 x ^ { 2 } + 1024 x$ 
C)  $V = x ^ { 3 } - 32 x ^ { 2 } + 256 x$ 
D)  $V = 16 x ^ { 2 } + 4 x ^ { 3 }$

Question 14

Suppose that the number of women, W, to be paid child support in the United States can be approximated by W(t) = 147t + 6780 where t is the number of years since the study began, and W(t) is the yearly total measured in thousands.
a. Evaluate W(0), W(5), and W(10).
b. Interpret the meaning of the function value W(10).

Accepted Answer

a. W(0) = 6780; W(5) = 7515; W

Question 15

A rectangular garden is to cover 468 square feet of area. If the width is 8 feet less than the length, find the dimensions of the pen.

Accepted Answer

A)  length = 52 ft; width = 9 ft 
B)  length = 26 ft; width = 18 ft 
C)  length = 27 ft; width = 19 ft 
D)  length = 28 ft; width = 20 ft 
A)  length = 52 ft; width = 9 ft 
B)  length = 26 ft; width = 18 ft 
C)  length = 27 ft; width = 19 ft 
D)  length = 28 ft; width = 20 ft

Question 16

Translate from algebraic form to English form. $$n ^ { 2 } + p ^ { 2 }$$

Accepted Answer

A)  The sum of n squared and p squared 
B)  The sum of the squares of n and p, squared 
C)  The square of the sum of n squared and p squared 
D)  The square of the sum of n and p 
A)  The sum of n squared and p squared 
B)  The sum of the squares of n and p, squared 
C)  The square of the sum of n squared and p squared 
D)  The square of the sum of n and p

Question 17

Divide by using synthetic division. $$\left( 6 t ^ { 3 } + 7 t ^ { 2 } - t + 5 \right) \div \left( t + \frac { 2 } { 3 } \right)$$

Accepted Answer

A)  $6 t ^ { 2 } + 3 t + 3$ 
B)  $6 t ^ { 2 } + 3 t - 3 + \frac { 7 } { t + \frac { 2 } { 3 } }$ 
C)  $6 t ^ { 2 } + 3 t - 3 + \frac { 21 } { t + \frac { 2 } { 3 } }$ 
D)  $6 t ^ { 2 } + 3 t + 4$ 
A)  $6 t ^ { 2 } + 3 t + 3$ 
B)  $6 t ^ { 2 } + 3 t - 3 + \frac { 7 } { t + \frac { 2 } { 3 } }$ 
C)  $6 t ^ { 2 } + 3 t - 3 + \frac { 21 } { t + \frac { 2 } { 3 } }$ 
D)  $6 t ^ { 2 } + 3 t + 4$

Question 18

Factor completely. $125 n ^ { 6 } - 8 p ^ { 6 }$

Accepted Answer

A)  $\left( 5 n ^ { 2 } - 2 p ^ { 2 } \right) \left( 25 n ^ { 4 } - 10 n ^ { 2 } p ^ { 2 } + 4 p ^ { 4 } \right)$ 
B)  $\left( 5 n ^ { 2 } - 2 p ^ { 2 } \right) \left( 25 n ^ { 4 } + 10 n ^ { 2 } p ^ { 2 } + 4 p ^ { 4 } \right)$ 
C)  $\left( 5 n ^ { 2 } + 2 p ^ { 2 } \right) \left( 25 n ^ { 4 } + 10 n ^ { 2 } p ^ { 2 } + 4 p ^ { 4 } \right)$ 
D)  Prime 
A)  $\left( 5 n ^ { 2 } - 2 p ^ { 2 } \right) \left( 25 n ^ { 4 } - 10 n ^ { 2 } p ^ { 2 } + 4 p ^ { 4 } \right)$ 
B)  $\left( 5 n ^ { 2 } - 2 p ^ { 2 } \right) \left( 25 n ^ { 4 } + 10 n ^ { 2 } p ^ { 2 } + 4 p ^ { 4 } \right)$ 
C)  $\left( 5 n ^ { 2 } + 2 p ^ { 2 } \right) \left( 25 n ^ { 4 } + 10 n ^ { 2 } p ^ { 2 } + 4 p ^ { 4 } \right)$ 
D)  Prime

Question 19

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $$f ( x ) = ( x - 2 ) ( x + 1 ) ( x + 2 )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

Multiply by using the special case products. $$\left( x - \frac { 1 } { 8 } \right) \left( x + \frac { 1 } { 8 } \right)$$

Accepted Answer

A)  $x ^ { 2 } + \frac { 2 } { 25 } x - \frac { 1 } { 64 }$ 
B)  $x ^ { 2 } - \frac { 2 } { 25 } x - \frac { 1 } { 64 }$ 
C)  $x ^ { 2 } + \frac { 1 } { 64 }$ 
D)  $x ^ { 2 } - \frac { 1 } { 64 }$ 
A)  $x ^ { 2 } + \frac { 2 } { 25 } x - \frac { 1 } { 64 }$ 
B)  $x ^ { 2 } - \frac { 2 } { 25 } x - \frac { 1 } { 64 }$ 
C)  $x ^ { 2 } + \frac { 1 } { 64 }$ 
D)  $x ^ { 2 } - \frac { 1 } { 64 }$

Divide the polynomials by using an appropriate method. $\left( s ^ { 4 } + 8 s ^ { 3 } + 2 s ^ { 2 } - 8 s - 5 \right) \div ( s + 1 )$

Translate from English form to algebraic form. The square of the difference of 2x + y and 8

Simplify the expression. Write your answer with positive exponents only. $\frac { z ^ { 2 } y ^ { 6 } } { y ^ { - 6 } z ^ { 9 } }$

Multiply the polynomials by using the distributive property. $( - 7.3 n + 4.7 p ) ( - 4.6 n + 3.1 p )$

Multiply by using the special case products. $\left( \frac { 2 } { 3 } w + 1 \right) ^ { 2 }$

Simplify the expression. Write your answer with positive exponents only. $\left( 2 x ^ { 6 } \right) ^ { 4 }$

Write the number in scientific notation. 0.00000063

Simplify the expression. Write your answer with positive exponents only. $y ^ { 8 } \cdot y ^ { 5 }$

Simplify. $\left( - \frac { 21 } { 16 } \right) ^ { 0 }$

Subtract the polynomials and simplify. $\left( - 3 r ^ { 2 } - 2 r - 4 \right) - \left( - 9 r ^ { 2 } + 7 r + 2 \right)$

Divide by using synthetic division. $\left( s ^ { 2 } + 12 s + 27 \right) \div ( s + 3 )$

The following table represents the result of a synthetic division. Use $x$ as the variable. Identify the dividend.

A box is created from a square piece of cardboard with sides measuring s = 16 cm by cutting a square from each corner and folding up the sides. Let x represent the length of the sides of the squares Removed from each corner. Find an expression representing the volume of the box.

A rectangular garden is to cover 468 square feet of area. If the width is 8 feet less than the length, find the dimensions of the pen.

Translate from algebraic form to English form. $n ^ { 2 } + p ^ { 2 }$

Divide by using synthetic division. $\left( 6 t ^ { 3 } + 7 t ^ { 2 } - t + 5 \right) \div \left( t + \frac { 2 } { 3 } \right)$

Factor completely. $125 n ^ { 6 } - 8 p ^ { 6 }$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $f ( x ) = ( x - 2 ) ( x + 1 ) ( x + 2 )$

Multiply by using the special case products. $\left( x - \frac { 1 } { 8 } \right) \left( x + \frac { 1 } { 8 } \right)$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

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Exam 4: Polynomials

Divide the polynomials by using an appropriate method. (s4+8s3+2s2−8s−5)÷(s+1)\left( s ^ { 4 } + 8 s ^ { 3 } + 2 s ^ { 2 } - 8 s - 5 \right) \div ( s + 1 )(s4+8s3+2s2−8s−5)÷(s+1)

Translate from English form to algebraic form. The square of the difference of 2x + y and 8

Simplify the expression. Write your answer with positive exponents only. z2y6y−6z9\frac { z ^ { 2 } y ^ { 6 } } { y ^ { - 6 } z ^ { 9 } }y−6z9z2y6​

Multiply the polynomials by using the distributive property. (−7.3n+4.7p)(−4.6n+3.1p)( - 7.3 n + 4.7 p ) ( - 4.6 n + 3.1 p )(−7.3n+4.7p)(−4.6n+3.1p)

Multiply by using the special case products. (23w+1)2\left( \frac { 2 } { 3 } w + 1 \right) ^ { 2 }(32​w+1)2

Simplify the expression. Write your answer with positive exponents only. (2x6)4\left( 2 x ^ { 6 } \right) ^ { 4 }(2x6)4

Write the number in scientific notation. 0.00000063

Simplify the expression. Write your answer with positive exponents only. y8⋅y5y ^ { 8 } \cdot y ^ { 5 }y8⋅y5

Simplify. (−2116)0\left( - \frac { 21 } { 16 } \right) ^ { 0 }(−1621​)0

Subtract the polynomials and simplify. (−3r2−2r−4)−(−9r2+7r+2)\left( - 3 r ^ { 2 } - 2 r - 4 \right) - \left( - 9 r ^ { 2 } + 7 r + 2 \right)(−3r2−2r−4)−(−9r2+7r+2)

Divide by using synthetic division. (s2+12s+27)÷(s+3)\left( s ^ { 2 } + 12 s + 27 \right) \div ( s + 3 )(s2+12s+27)÷(s+3)

The following table represents the result of a synthetic division. Use xxx as the variable. Identify the dividend.

A box is created from a square piece of cardboard with sides measuring s = 16 cm by cutting a square from each corner and folding up the sides. Let x represent the length of the sides of the squares Removed from each corner. Find an expression representing the volume of the box.

A rectangular garden is to cover 468 square feet of area. If the width is 8 feet less than the length, find the dimensions of the pen.

Translate from algebraic form to English form. n2+p2n ^ { 2 } + p ^ { 2 }n2+p2

Divide by using synthetic division. (6t3+7t2−t+5)÷(t+23)\left( 6 t ^ { 3 } + 7 t ^ { 2 } - t + 5 \right) \div \left( t + \frac { 2 } { 3 } \right)(6t3+7t2−t+5)÷(t+32​)

Factor completely. 125n6−8p6125 n ^ { 6 } - 8 p ^ { 6 }125n6−8p6

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. f(x)=(x−2)(x+1)(x+2)f ( x ) = ( x - 2 ) ( x + 1 ) ( x + 2 )f(x)=(x−2)(x+1)(x+2)

Multiply by using the special case products. (x−18)(x+18)\left( x - \frac { 1 } { 8 } \right) \left( x + \frac { 1 } { 8 } \right)(x−81​)(x+81​)

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Divide the polynomials by using an appropriate method. $\left( s ^ { 4 } + 8 s ^ { 3 } + 2 s ^ { 2 } - 8 s - 5 \right) \div ( s + 1 )$

Simplify the expression. Write your answer with positive exponents only. $\frac { z ^ { 2 } y ^ { 6 } } { y ^ { - 6 } z ^ { 9 } }$

Multiply the polynomials by using the distributive property. $( - 7.3 n + 4.7 p ) ( - 4.6 n + 3.1 p )$

Multiply by using the special case products. $\left( \frac { 2 } { 3 } w + 1 \right) ^ { 2 }$

Simplify the expression. Write your answer with positive exponents only. $\left( 2 x ^ { 6 } \right) ^ { 4 }$

Simplify the expression. Write your answer with positive exponents only. $y ^ { 8 } \cdot y ^ { 5 }$

Simplify. $\left( - \frac { 21 } { 16 } \right) ^ { 0 }$

Subtract the polynomials and simplify. $\left( - 3 r ^ { 2 } - 2 r - 4 \right) - \left( - 9 r ^ { 2 } + 7 r + 2 \right)$

Divide by using synthetic division. $\left( s ^ { 2 } + 12 s + 27 \right) \div ( s + 3 )$

The following table represents the result of a synthetic division. Use $x$ as the variable. Identify the dividend.

Translate from algebraic form to English form. $n ^ { 2 } + p ^ { 2 }$

Divide by using synthetic division. $\left( 6 t ^ { 3 } + 7 t ^ { 2 } - t + 5 \right) \div \left( t + \frac { 2 } { 3 } \right)$

Factor completely. $125 n ^ { 6 } - 8 p ^ { 6 }$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $f ( x ) = ( x - 2 ) ( x + 1 ) ( x + 2 )$

Multiply by using the special case products. $\left( x - \frac { 1 } { 8 } \right) \left( x + \frac { 1 } { 8 } \right)$