Question 1

Solve the equation. $$2 q ( q + 9 ) ^ { 2 } ( 6 q - 5 ) = 0$$

Accepted Answer

A)  $q = - 9 ; q = \frac { 5 } { 6 }$ 
B)  $q = 0 ; q = 9 ; q = q = - 5$ 
C)  $q = 0 ; q = - 9 ; q = \frac { 5 } { 6 }$ 
D)  $q = 0 ; q = 9 ; q = - \frac { 5 } { 6 }$ 
A)  $q = - 9 ; q = \frac { 5 } { 6 }$ 
B)  $q = 0 ; q = 9 ; q = q = - 5$ 
C)  $q = 0 ; q = - 9 ; q = \frac { 5 } { 6 }$ 
D)  $q = 0 ; q = 9 ; q = - \frac { 5 } { 6 }$

Question 2

Complete the property of exponents. $( a b ) ^ { n } =$______

Accepted Answer

A)  $a ^ { n } b ^ { n }$ 
B)  $a ^ { n } b$ 
C)  $a b ^ { n }$ 
D)  $a ^ { n } + b ^ { n }$ 
A)  $a ^ { n } b ^ { n }$ 
B)  $a ^ { n } b$ 
C)  $a b ^ { n }$ 
D)  $a ^ { n } + b ^ { n }$

Question 3

Multiply by using the special case products. $$( 2 r + 2 ) ( 2 r - 2 )$$

Accepted Answer

A)  $4 r ^ { 2 } - 4$ 
B)  $4 r ^ { 2 } + 8 x + 4$ 
C)  $4 r ^ { 2 } + 4$ 
D)  $4 r ^ { 2 } - 8 x + 4$ 
A)  $4 r ^ { 2 } - 4$ 
B)  $4 r ^ { 2 } + 8 x + 4$ 
C)  $4 r ^ { 2 } + 4$ 
D)  $4 r ^ { 2 } - 8 x + 4$

Question 4

The following table represents the result of a synthetic division.

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

Accepted Answer

A)  $- 25$ 
B)  $2 x ^ { 2 } - 4 x - 15$ 
C)  $x - 2$ 
D)  $2 x ^ { 3 } - 8 x ^ { 2 } - 7 x + 5$ 
A)  $- 25$ 
B)  $2 x ^ { 2 } - 4 x - 15$ 
C)  $x - 2$ 
D)  $2 x ^ { 3 } - 8 x ^ { 2 } - 7 x + 5$

Question 5

Add or subtract as indicated. $$\left( - 7 p ^ { 4 } q ^ { 2 } + 2 p ^ { 3 } q \right) - \left[ 2 p ^ { 4 } q ^ { 2 } - 3 p q - \left( 7 p ^ { 3 } q + 6 p q \right) \right]$$

Accepted Answer

A)  $- 9 p ^ { 4 } q ^ { 2 } + 9 p ^ { 3 } q + 9 p q$ 
B)  $- 9 p ^ { 4 } q ^ { 2 } - 5 p ^ { 3 } q - 3 p q$ 
C)  $- 9 p ^ { 4 } q ^ { 2 } + 2 p ^ { 3 } q - 3 p q$ 
D)  $- 9 p ^ { 4 } q ^ { 2 } + 9 p ^ { 3 } q - 3 p q$ 
A)  $- 9 p ^ { 4 } q ^ { 2 } + 9 p ^ { 3 } q + 9 p q$ 
B)  $- 9 p ^ { 4 } q ^ { 2 } - 5 p ^ { 3 } q - 3 p q$ 
C)  $- 9 p ^ { 4 } q ^ { 2 } + 2 p ^ { 3 } q - 3 p q$ 
D)  $- 9 p ^ { 4 } q ^ { 2 } + 9 p ^ { 3 } q - 3 p q$

Question 6

Factor by using substitution. $$( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24$$

Accepted Answer

A)  $5 ( 5 x + 1 ) ( x - 2 )$ 
B)  $5 ( 5 x - 1 ) ( x + 2 )$ 
C)  $5 ( 5 x - 1 ) ( x - 2 )$ 
D)  Prime 
A)  $5 ( 5 x + 1 ) ( x - 2 )$ 
B)  $5 ( 5 x - 1 ) ( x + 2 )$ 
C)  $5 ( 5 x - 1 ) ( x - 2 )$ 
D)  Prime

Question 7

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $$\mathrm { h } ( \mathrm { x } ) = x ( x + 1 ) ( x - 2 ) ( x - 4 )$$

Accepted Answer

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

Question 8

Perform the indicated operation, and write your answer in scientific notation. Round the final answer to one decimal place. $$\left( 1.9 \times 10 ^ { - 5 } \right) \div \left( 3.4 \times 10 ^ { - 11 } \right)$$

Accepted Answer

A)  $0.6 \times 10 ^ { - 16 }$ 
B)  $0.6 \times 10 ^ { 6 }$ 
C)  $5.6 \times 100 ^ { - 16 }$ 
D)  $5.6 \times 10 ^ { 5 }$ 
A)  $0.6 \times 10 ^ { - 16 }$ 
B)  $0.6 \times 10 ^ { 6 }$ 
C)  $5.6 \times 100 ^ { - 16 }$ 
D)  $5.6 \times 10 ^ { 5 }$

Question 9

Complete the property of exponents. $$\frac { b ^ { n } } { b ^ { m } } =........  { ( b \neq 0 ) }$$

Accepted Answer

A)  $b ^ { n + m }$ 
B)  $b ^ { n } - b ^ { m }$ 
C)  $b ^ { n / m }$ 
D)  $b ^ { n - m }$ 
A)  $b ^ { n + m }$ 
B)  $b ^ { n } - b ^ { m }$ 
C)  $b ^ { n / m }$ 
D)  $b ^ { n - m }$

Question 10

Factor the trinomial completely by using any method. Remember to look for a common factor first. $7 u ^ { 2 } - 2 u + 4$

Accepted Answer

A)  Prime 
B)  $u ( 7 u - 2 ) + 4$ 
C)  $( 7 u + 4 ) ( u + 2 )$ 
D)  $( 7 u - 4 ) ( u - 2 )$ 
A)  Prime 
B)  $u ( 7 u - 2 ) + 4$ 
C)  $( 7 u + 4 ) ( u + 2 )$ 
D)  $( 7 u - 4 ) ( u - 2 )$

Question 11

Divide the polynomials by using an appropriate method. $$\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)$$

Accepted Answer

A)  $- 8 n + 3 + \frac { 3 n } { 6 n ^ { 2 } + 4 n + 1 }$ 
B)  $- 8 n + 3 + \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$ 
C)  $- 8 n + 3 - \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$ 
D)  $- 8 n - 3$ 
A)  $- 8 n + 3 + \frac { 3 n } { 6 n ^ { 2 } + 4 n + 1 }$ 
B)  $- 8 n + 3 + \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$ 
C)  $- 8 n + 3 - \frac { 3 n + 8 } { 6 n ^ { 2 } + 4 n + 1 }$ 
D)  $- 8 n - 3$

Question 12

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $$y ^ { 2 } - 12 y + 36$$

Accepted Answer

A)  $( y - 12 ) ^ { 2 }$ 
B)  $( y + 6 ) ^ { 2 }$ 
C)  $( y - 6 ) ^ { 2 }$ 
D)  Not a perfect square trinomial 
A)  $( y - 12 ) ^ { 2 }$ 
B)  $( y + 6 ) ^ { 2 }$ 
C)  $( y - 6 ) ^ { 2 }$ 
D)  Not a perfect square trinomial

Question 13

Factor the polynomial by grouping (if possible). $4 a u + 12 b u + 3 a c - 9 b c$

Accepted Answer

A)  $4 u ( a + 3 b ) + 3 c ( a - 3 b )$ 
B)  $( 4 u - 3 c ) ( a - 3 b )$ 
C)  $( 4 u + 3 c ) ( a + 3 b )$ 
D)  Cannot be factored 
A)  $4 u ( a + 3 b ) + 3 c ( a - 3 b )$ 
B)  $( 4 u - 3 c ) ( a - 3 b )$ 
C)  $( 4 u + 3 c ) ( a + 3 b )$ 
D)  Cannot be factored

Question 14

Given $H ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 3 x ^ { 2 } + \frac { 1 } { 4 }$, find the function value.
$H ( 1 )$

Accepted Answer

A)  $- \frac { 9 } { 4 }$ 
B)  $\frac { 15 } { 4 }$ 
C)  $\frac { 11 } { 4 }$ 
D)  $\frac { 9 } { 4 }$ 
A)  $- \frac { 9 } { 4 }$ 
B)  $\frac { 15 } { 4 }$ 
C)  $\frac { 11 } { 4 }$ 
D)  $\frac { 9 } { 4 }$

Question 15

Factor by using substitution. $$4 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 8$$

Accepted Answer

A)  $( 4 t + 2 ) ( t + 4 )$ 
B)  $2 ( 8 t - 1 ) ( 4 t + 3 )$ 
C)  $2 ( 8 t + 1 ) ( 4 t - 3 )$ 
D)  Prime 
A)  $( 4 t + 2 ) ( t + 4 )$ 
B)  $2 ( 8 t - 1 ) ( 4 t + 3 )$ 
C)  $2 ( 8 t + 1 ) ( 4 t - 3 )$ 
D)  Prime

Question 16

Simplify the expression. Write your answer with positive exponents only. $$\left( \frac { 2 x ^ { - 4 } y ^ { 5 } } { 5 x ^ { 4 } y ^ { - 7 } } \right) ^ { - 3 }$$

Accepted Answer

The answer of Simplify the expression. Write your answer with...

Question 17

Translate from algebraic form to English form. $$( w + x ) ^ { 2 }$$

Accepted Answer

A)  The sum of w squared and x squared 
B)  The square of the sum of w and x 
C)  The square of the sum of w squared and x squared 
D)  The sum of the squares of w and x, squared 
A)  The sum of w squared and x squared 
B)  The square of the sum of w and x 
C)  The square of the sum of w squared and x squared 
D)  The sum of the squares of w and x, squared

Question 18

Factor the trinomial completely by using any method. Remember to look for a common factor first. $5 w ^ { 2 } - 7 w - 3$

Accepted Answer

A)  $w ( 5 w - 7 ) - 3$ 
B)  Prime 
C)  $( 5 w + 3 ) ( w - 7 )$ 
D)  $( 5 w - 7 ) ( w + 3 )$ 
A)  $w ( 5 w - 7 ) - 3$ 
B)  Prime 
C)  $( 5 w + 3 ) ( w - 7 )$ 
D)  $( 5 w - 7 ) ( w + 3 )$

Question 19

The following table represents the result of a synthetic division.

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

Accepted Answer

A)  $- 6 x ^ { 3 } - 7 x ^ { 2 } - 7 x + 6$ 
B)  $- 14$ 
C)  $x + 1$ 
D)  $x - 1$ 
A)  $- 6 x ^ { 3 } - 7 x ^ { 2 } - 7 x + 6$ 
B)  $- 14$ 
C)  $x + 1$ 
D)  $x - 1$

Question 20

Perform the indicated operation and write the answer in scientific notation. $\left( 1.7 \times 10 ^ { 6 } \right) \left( 3.1 \times 10 ^ { 10 } \right)$

Accepted Answer

A)  $4.8 \times 10 ^ { 16 }$ 
B)  $5.27 \times 10 ^ { 60 }$ 
C)  $5.27 \times 10 ^ { 16 }$ 
D)  $5.27 \times 100 ^ { 16 }$ 
A)  $4.8 \times 10 ^ { 16 }$ 
B)  $5.27 \times 10 ^ { 60 }$ 
C)  $5.27 \times 10 ^ { 16 }$ 
D)  $5.27 \times 100 ^ { 16 }$

Solve the equation. $2 q ( q + 9 ) ^ { 2 } ( 6 q - 5 ) = 0$

Complete the property of exponents. $( a b ) ^ { n } =$ ______

Multiply by using the special case products. $( 2 r + 2 ) ( 2 r - 2 )$

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

Add or subtract as indicated. $\left( - 7 p ^ { 4 } q ^ { 2 } + 2 p ^ { 3 } q \right) - \left[ 2 p ^ { 4 } q ^ { 2 } - 3 p q - \left( 7 p ^ { 3 } q + 6 p q \right) \right]$

Factor by using substitution. $( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $\mathrm { h } ( \mathrm { x } ) = x ( x + 1 ) ( x - 2 ) ( x - 4 )$

Perform the indicated operation, and write your answer in scientific notation. Round the final answer to one decimal place. $\left( 1.9 \times 10 ^ { - 5 } \right) \div \left( 3.4 \times 10 ^ { - 11 } \right)$

Complete the property of exponents. $\frac { b ^ { n } } { b ^ { m } } =........ { ( b \neq 0 ) }$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $7 u ^ { 2 } - 2 u + 4$

Divide the polynomials by using an appropriate method. $\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $y ^ { 2 } - 12 y + 36$

Factor the polynomial by grouping (if possible). $4 a u + 12 b u + 3 a c - 9 b c$

Given $H ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 3 x ^ { 2 } + \frac { 1 } { 4 }$ , find the function value. $H ( 1 )$

Factor by using substitution. $4 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 8$

Simplify the expression. Write your answer with positive exponents only. $\left( \frac { 2 x ^ { - 4 } y ^ { 5 } } { 5 x ^ { 4 } y ^ { - 7 } } \right) ^ { - 3 }$

Translate from algebraic form to English form. $( w + x ) ^ { 2 }$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $5 w ^ { 2 } - 7 w - 3$

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

Perform the indicated operation and write the answer in scientific notation. $\left( 1.7 \times 10 ^ { 6 } \right) \left( 3.1 \times 10 ^ { 10 } \right)$

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Exam 4: Polynomials

Solve the equation. 2q(q+9)2(6q−5)=02 q ( q + 9 ) ^ { 2 } ( 6 q - 5 ) = 02q(q+9)2(6q−5)=0

Complete the property of exponents. (ab)n=( a b ) ^ { n } =(ab)n= ______

Multiply by using the special case products. (2r+2)(2r−2)( 2 r + 2 ) ( 2 r - 2 )(2r+2)(2r−2)

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

Add or subtract as indicated. (−7p4q2+2p3q)−[2p4q2−3pq−(7p3q+6pq)]\left( - 7 p ^ { 4 } q ^ { 2 } + 2 p ^ { 3 } q \right) - \left[ 2 p ^ { 4 } q ^ { 2 } - 3 p q - \left( 7 p ^ { 3 } q + 6 p q \right) \right](−7p4q2+2p3q)−[2p4q2−3pq−(7p3q+6pq)]

Factor by using substitution. (5x+7)2−5(5x+7)−24( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24(5x+7)2−5(5x+7)−24

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. h(x)=x(x+1)(x−2)(x−4)\mathrm { h } ( \mathrm { x } ) = x ( x + 1 ) ( x - 2 ) ( x - 4 )h(x)=x(x+1)(x−2)(x−4)

Perform the indicated operation, and write your answer in scientific notation. Round the final answer to one decimal place. (1.9×10−5)÷(3.4×10−11)\left( 1.9 \times 10 ^ { - 5 } \right) \div \left( 3.4 \times 10 ^ { - 11 } \right)(1.9×10−5)÷(3.4×10−11)

Complete the property of exponents. bnbm=........(b≠0)\frac { b ^ { n } } { b ^ { m } } =........ { ( b \neq 0 ) }bmbn​=........(b=0)

Factor the trinomial completely by using any method. Remember to look for a common factor first. 7u2−2u+47 u ^ { 2 } - 2 u + 47u2−2u+4

Divide the polynomials by using an appropriate method. (−48n3−14n2+7n+11)÷(6n2+4n+1)\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)(−48n3−14n2+7n+11)÷(6n2+4n+1)

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. y2−12y+36y ^ { 2 } - 12 y + 36y2−12y+36

Factor the polynomial by grouping (if possible). 4au+12bu+3ac−9bc4 a u + 12 b u + 3 a c - 9 b c4au+12bu+3ac−9bc

Given H(x)=12x3−3x2+14H ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 3 x ^ { 2 } + \frac { 1 } { 4 }H(x)=21​x3−3x2+41​ , find the function value. H(1)H ( 1 )H(1)

Factor by using substitution. 4(4t−1)2+18(4t−1)+84 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 84(4t−1)2+18(4t−1)+8

Simplify the expression. Write your answer with positive exponents only. (2x−4y55x4y−7)−3\left( \frac { 2 x ^ { - 4 } y ^ { 5 } } { 5 x ^ { 4 } y ^ { - 7 } } \right) ^ { - 3 }(5x4y−72x−4y5​)−3

Translate from algebraic form to English form. (w+x)2( w + x ) ^ { 2 }(w+x)2

Factor the trinomial completely by using any method. Remember to look for a common factor first. 5w2−7w−35 w ^ { 2 } - 7 w - 35w2−7w−3

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

Perform the indicated operation and write the answer in scientific notation. (1.7×106)(3.1×1010)\left( 1.7 \times 10 ^ { 6 } \right) \left( 3.1 \times 10 ^ { 10 } \right)(1.7×106)(3.1×1010)

Linear Equations and Inequalities in One Variable

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Solve the equation. $2 q ( q + 9 ) ^ { 2 } ( 6 q - 5 ) = 0$

Complete the property of exponents. $( a b ) ^ { n } =$ ______

Multiply by using the special case products. $( 2 r + 2 ) ( 2 r - 2 )$

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

Add or subtract as indicated. $\left( - 7 p ^ { 4 } q ^ { 2 } + 2 p ^ { 3 } q \right) - \left[ 2 p ^ { 4 } q ^ { 2 } - 3 p q - \left( 7 p ^ { 3 } q + 6 p q \right) \right]$

Factor by using substitution. $( 5 x + 7 ) ^ { 2 } - 5 ( 5 x + 7 ) - 24$

Find the x-intercepts of the function and use that information to decide which of the following could be its graph. $\mathrm { h } ( \mathrm { x } ) = x ( x + 1 ) ( x - 2 ) ( x - 4 )$

Perform the indicated operation, and write your answer in scientific notation. Round the final answer to one decimal place. $\left( 1.9 \times 10 ^ { - 5 } \right) \div \left( 3.4 \times 10 ^ { - 11 } \right)$

Complete the property of exponents. $\frac { b ^ { n } } { b ^ { m } } =........ { ( b \neq 0 ) }$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $7 u ^ { 2 } - 2 u + 4$

Divide the polynomials by using an appropriate method. $\left( - 48 n ^ { 3 } - 14 n ^ { 2 } + 7 n + 11 \right) \div \left( 6 n ^ { 2 } + 4 n + 1 \right)$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $y ^ { 2 } - 12 y + 36$

Factor the polynomial by grouping (if possible). $4 a u + 12 b u + 3 a c - 9 b c$

Given $H ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 3 x ^ { 2 } + \frac { 1 } { 4 }$ , find the function value. $H ( 1 )$

Factor by using substitution. $4 ( 4 t - 1 ) ^ { 2 } + 18 ( 4 t - 1 ) + 8$

Simplify the expression. Write your answer with positive exponents only. $\left( \frac { 2 x ^ { - 4 } y ^ { 5 } } { 5 x ^ { 4 } y ^ { - 7 } } \right) ^ { - 3 }$

Translate from algebraic form to English form. $( w + x ) ^ { 2 }$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $5 w ^ { 2 } - 7 w - 3$

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

Perform the indicated operation and write the answer in scientific notation. $\left( 1.7 \times 10 ^ { 6 } \right) \left( 3.1 \times 10 ^ { 10 } \right)$