Question 1

Factor completely. $$125 w ^ { 3 } + \frac { 1 } { 27 }$$

Accepted Answer

A)  $\left( 5 w + \frac { 1 } { 3 } \right) \left( 25 w ^ { 2 } - \frac { 5 } { 3 } w + \frac { 1 } { 9 } \right)$ 
B)  $\left( 5 w - \frac { 1 } { 3 } \right) \left( 25 w ^ { 2 } + \frac { 5 } { 3 } w + \frac { 1 } { 9 } \right)$ 
C)  $\left( 5 w + \frac { 1 } { 3 } \right) \left( 25 w ^ { 2 } - \frac { 10 } { 3 } w + \frac { 1 } { 9 } \right)$ 
D)  Prime 
A)  $\left( 5 w + \frac { 1 } { 3 } \right) \left( 25 w ^ { 2 } - \frac { 5 } { 3 } w + \frac { 1 } { 9 } \right)$ 
B)  $\left( 5 w - \frac { 1 } { 3 } \right) \left( 25 w ^ { 2 } + \frac { 5 } { 3 } w + \frac { 1 } { 9 } \right)$ 
C)  $\left( 5 w + \frac { 1 } { 3 } \right) \left( 25 w ^ { 2 } - \frac { 10 } { 3 } w + \frac { 1 } { 9 } \right)$ 
D)  Prime

Question 2

The height of a triangle is 2 feet more than 2 times the base. If the area is 42 ft2, find the base and height of the triangle.

Accepted Answer

A)  height = 13 ft; base = 5 ft 
B)  height = 28 ft; base = 6 ft 
C)  height = 28 ft; base = 3 ft 
D)  height = 14 ft; base = 6 ft 
A)  height = 13 ft; base = 5 ft 
B)  height = 28 ft; base = 6 ft 
C)  height = 28 ft; base = 3 ft 
D)  height = 14 ft; base = 6 ft

Question 3

Add the polynomials and simplify. $$\left( \frac { 5 } { 6 } w ^ { 3 } + \frac { 9 } { 8 } w ^ { 2 } - 3.8 w \right) + \left( - \frac { 7 } { 6 } w ^ { 3 } - \frac { 1 } { 4 } w ^ { 2 } - 3.4 w \right)$$

Accepted Answer

A)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 11 } { 8 } w ^ { 2 } - 7.2 w$ 
B)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 11 } { 8 } w ^ { 2 } - 0.4 w$ 
C)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 7 } { 8 } w ^ { 2 } - 7.2 w$ 
D)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 7 } { 8 } w ^ { 2 } - 0.4 w$ 
A)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 11 } { 8 } w ^ { 2 } - 7.2 w$ 
B)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 11 } { 8 } w ^ { 2 } - 0.4 w$ 
C)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 7 } { 8 } w ^ { 2 } - 7.2 w$ 
D)  $- \frac { 1 } { 3 } w ^ { 3 } + \frac { 7 } { 8 } w ^ { 2 } - 0.4 w$

Question 4

Multiply the expressions. $$[ ( 4 x + 4 ) + y ] [ ( 4 x + 4 ) - y ]$$

Accepted Answer

A)  $16 x ^ { 2 } + 32 x + 16 - y ^ { 2 }$ 
B)  $16 x ^ { 2 } + 16 - y ^ { 2 }$ 
C)  $16 x ^ { 2 } + 64 x + 16 - y ^ { 2 }$ 
D)  $16 x ^ { 2 } + 32 x + 8 x y + 16 + 7 y ^ { 2 }$ 
A)  $16 x ^ { 2 } + 32 x + 16 - y ^ { 2 }$ 
B)  $16 x ^ { 2 } + 16 - y ^ { 2 }$ 
C)  $16 x ^ { 2 } + 64 x + 16 - y ^ { 2 }$ 
D)  $16 x ^ { 2 } + 32 x + 8 x y + 16 + 7 y ^ { 2 }$

Question 5

Determine which number is in "proper" scientific notation.

Accepted Answer

A)  $0.5 \times 10 ^ { 8 }$ 
B)  $49 \times 10 ^ { 5 }$ 
C)  $2.31 \times 10 ^ { - 4 }$ 
D)  $0.98 \times 10 ^ { 10 }$ 
A)  $0.5 \times 10 ^ { 8 }$ 
B)  $49 \times 10 ^ { 5 }$ 
C)  $2.31 \times 10 ^ { - 4 }$ 
D)  $0.98 \times 10 ^ { 10 }$

Question 6

Divide the polynomials. $$\frac { - 6 x ^ { 3 } + 4 x ^ { 2 } - 4 x } { - 2 x }$$

Accepted Answer

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

Question 7

A patient's response to an experimental fever-reducing drug can be modeled with the function $D ( t ) = 0.025 t ^ { 2 } - 0.4 t$ where t is the time in hours after taking a dose of the medication and D(t) represents the change in the patient's body temperature in Celsius degrees (see graph).   a. What characteristics of D indicate that it is a quadratic function?
b. Find the times at which there is no fever reduction.
c. What points on the graph do the answers in part (b) represent?
d. At what times has the patient's temperature been reduced by 1.2°? [Hint: be sure to choose the correct sign for the temperature change. A reduction in temperature suggests what sign for the temperature change D(t)?]

Accepted Answer

a. @#LAT-DLM& is of the form @#LAT-DLM&.
b. There

Question 8

Simplify. $6 ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { 1296 }$ 
B)  $- 24$ 
C)  $- 1296$ 
D)  2 
A)  $\frac { 1 } { 1296 }$ 
B)  $- 24$ 
C)  $- 1296$ 
D)  2

Question 9

Translate from algebraic form to English form. $$9 a ^ { 3 }$$

Accepted Answer

A)  The product of 9 and the square of a 
B)  The product of 9 and the cube of a 
C)  The product of 9 and a, cubed 
D)  The product of 9 and the cube root of a 
A)  The product of 9 and the square of a 
B)  The product of 9 and the cube of a 
C)  The product of 9 and a, cubed 
D)  The product of 9 and the cube root of a

Question 10

Carol needs to travel to Stoney Point from her home in Collinsville. She can travel 39 miles via a rural route at 45 mph, or she can travel a somewhat longer distance at 65 mph if she follows one Interstate due east and then another interstate due north (see figure). If the eastern portion of the
Interstate route is 21 miles less than the northern portion, find the total distance Carol will travel if She follows the interstate route.   [Figure is not necessarily drawn to scale.]

Accepted Answer

A)  61 miles 
B)  17 miles 
C)  12 miles 
D)  51 miles 
A)  61 miles 
B)  17 miles 
C)  12 miles 
D)  51 miles

Question 11

Factor the sum or difference of cubes. $$27 m ^ { 3 } + 125 n ^ { 3 }$$

Accepted Answer

A)  $( 3 m - 5 n ) \left( 9 m ^ { 2 } + 15 m n + 25 n ^ { 2 } \right)$ 
B)  $( 3 m + 5 n ) ^ { 2 } ( 3 m - 5 n )$ 
C)  $( 3 m + 5 n ) \left( 9 m ^ { 2 } - 30 m n + 25 n ^ { 2 } \right)$ 
D)  $( 3 m + 5 n ) \left( 9 m ^ { 2 } - 15 m n + 25 n ^ { 2 } \right)$ 
A)  $( 3 m - 5 n ) \left( 9 m ^ { 2 } + 15 m n + 25 n ^ { 2 } \right)$ 
B)  $( 3 m + 5 n ) ^ { 2 } ( 3 m - 5 n )$ 
C)  $( 3 m + 5 n ) \left( 9 m ^ { 2 } - 30 m n + 25 n ^ { 2 } \right)$ 
D)  $( 3 m + 5 n ) \left( 9 m ^ { 2 } - 15 m n + 25 n ^ { 2 } \right)$

Question 12

Write the number in standard notation. $$6.5 \times 10 ^ { - 7 }$$

Accepted Answer

A)  65,000,000 
B)  0.000000065 
C)  0.0000065 
D)  0.00000065 
A)  65,000,000 
B)  0.000000065 
C)  0.0000065 
D)  0.00000065

Question 13

Solve the equation. $$r ^ { 3 } = 36 r$$

Accepted Answer

A)  $r = 0 ; r = 6$ 
B)  $r = 0 ; r = 36$ 
C)  $r = 0 ; r = 6 ; r = - 6$ 
D)  $r = 6 ; r = - 6$ 
A)  $r = 0 ; r = 6$ 
B)  $r = 0 ; r = 36$ 
C)  $r = 0 ; r = 6 ; r = - 6$ 
D)  $r = 6 ; r = - 6$

Question 14

Factor out the greatest common factor. $$20 w ^ { 3 } + 70 w ^ { 2 }$$

Accepted Answer

A)  $10 \left( 2 w ^ { 3 } + 7 w ^ { 2 } \right)$ 
B)  $10 w ^ { 2 } \left( 2 w + 70 w ^ { 2 } \right)$ 
C)  $2 w ^ { 2 } ( 10 w + 35 )$ 
D)  $10 w ^ { 2 } ( 2 w + 7 )$ 
A)  $10 \left( 2 w ^ { 3 } + 7 w ^ { 2 } \right)$ 
B)  $10 w ^ { 2 } \left( 2 w + 70 w ^ { 2 } \right)$ 
C)  $2 w ^ { 2 } ( 10 w + 35 )$ 
D)  $10 w ^ { 2 } ( 2 w + 7 )$

Question 15

Simplify the expression. Write your answer with positive exponents only. $6 ^ { 4 } \cdot 6 ^ { 7 }$

Accepted Answer

A)  $6 ^ { - 3 }$ 
B)  $36 ^ { 11 }$ 
C)  $6 ^ { 28 }$ 
D)  $6 ^ { 11 }$ 
A)  $6 ^ { - 3 }$ 
B)  $36 ^ { 11 }$ 
C)  $6 ^ { 28 }$ 
D)  $6 ^ { 11 }$

Question 16

Multiply the polynomials by using the distributive property. $$( 8 w + 7 ) ( w - 7 )$$

Accepted Answer

A)  $9 w ^ { 2 } - 49 w - 49$ 
B)  $8 w ^ { 2 } - 63 w - 49$ 
C)  $8 w ^ { 2 } - 49 w - 49$ 
D)  $8 w ^ { 2 } - 49$ 
A)  $9 w ^ { 2 } - 49 w - 49$ 
B)  $8 w ^ { 2 } - 63 w - 49$ 
C)  $8 w ^ { 2 } - 49 w - 49$ 
D)  $8 w ^ { 2 } - 49$

Question 17

Factor the polynomial by grouping (if possible). $2 x ^ { 5 } - 4 x ^ { 4 } + 4 x ^ { 3 } - 8 x ^ { 2 }$

Accepted Answer

A)  $\left( 2 x ^ { 3 } - 4 x ^ { 2 } \right) \left( x ^ { 2 } + 2 \right)$ 
B)  $2 x ^ { 2 } ( x - 2 ) \left( x ^ { 2 } + 2 \right)$ 
C)  $2 x ^ { 4 } ( x - 2 ) + 4 x ^ { 2 } ( x - 2 )$ 
D)  Cannot be factored 
A)  $\left( 2 x ^ { 3 } - 4 x ^ { 2 } \right) \left( x ^ { 2 } + 2 \right)$ 
B)  $2 x ^ { 2 } ( x - 2 ) \left( x ^ { 2 } + 2 \right)$ 
C)  $2 x ^ { 4 } ( x - 2 ) + 4 x ^ { 2 } ( x - 2 )$ 
D)  Cannot be factored

Question 18

Factor the function represented by f (x) and explain how the factored form relates to the graph of the function. $f ( x ) = x ^ { 2 } - 4 x - 21$

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x - 7 ) ; x = - 3$ and $x = 7$ represent the $y$-intercepts. 
B)  $f ( x ) = ( x - 3 ) ( x + 7 ) ; x = 3$ and $x = - 7$ represent the $x$-intercepts. 
C)  $f ( x ) = ( x - 3 ) ( x + 7 ) ; x = 3$ and $x = - 7$ represent the $y$-intercepts. 
D)  $f ( x ) = ( x + 3 ) ( x - 7 ) ; x = - 3$ and $x = 7$ represent the $x$-intercepts. 
A)  $f ( x ) = ( x + 3 ) ( x - 7 ) ; x = - 3$ and $x = 7$ represent the $y$-intercepts. 
B)  $f ( x ) = ( x - 3 ) ( x + 7 ) ; x = 3$ and $x = - 7$ represent the $x$-intercepts. 
C)  $f ( x ) = ( x - 3 ) ( x + 7 ) ; x = 3$ and $x = - 7$ represent the $y$-intercepts. 
D)  $f ( x ) = ( x + 3 ) ( x - 7 ) ; x = - 3$ and $x = 7$ represent the $x$-intercepts.

Question 19

Write the number in standard notation. $$8.6 \times 10 ^ { 6 }$$

Accepted Answer

The answer of Write the number in standard notation. \[8.6...

Question 20

Factor out the greatest common factor. $30 t ^ { 2 } u + 12 t u ^ { 2 } + 24 t u$

Accepted Answer

A)  $6 t u ( 5 t + 2 u + 4 )$ 
B)  $3 t u ( 10 t + 4 u + 8 )$ 
C)  $6 \mathrm { t } \left( 5 \mathrm { tu } + 2 u ^ { 2 } + 4 \right)$ 
D)  $2 t u ( 15 t + 6 u + 12 )$ 
A)  $6 t u ( 5 t + 2 u + 4 )$ 
B)  $3 t u ( 10 t + 4 u + 8 )$ 
C)  $6 \mathrm { t } \left( 5 \mathrm { tu } + 2 u ^ { 2 } + 4 \right)$ 
D)  $2 t u ( 15 t + 6 u + 12 )$

Factor completely. $125 w ^ { 3 } + \frac { 1 } { 27 }$

The height of a triangle is 2 feet more than 2 times the base. If the area is 42 ft², find the base and height of the triangle.

Add the polynomials and simplify. $\left( \frac { 5 } { 6 } w ^ { 3 } + \frac { 9 } { 8 } w ^ { 2 } - 3.8 w \right) + \left( - \frac { 7 } { 6 } w ^ { 3 } - \frac { 1 } { 4 } w ^ { 2 } - 3.4 w \right)$

Multiply the expressions. $[ ( 4 x + 4 ) + y ] [ ( 4 x + 4 ) - y ]$

Determine which number is in "proper" scientific notation.

Divide the polynomials. $\frac { - 6 x ^ { 3 } + 4 x ^ { 2 } - 4 x } { - 2 x }$

Simplify. $6 ^ { - 4 }$

Translate from algebraic form to English form. $9 a ^ { 3 }$

Factor the sum or difference of cubes. $27 m ^ { 3 } + 125 n ^ { 3 }$

Write the number in standard notation. $6.5 \times 10 ^ { - 7 }$

Solve the equation. $r ^ { 3 } = 36 r$

Factor out the greatest common factor. $20 w ^ { 3 } + 70 w ^ { 2 }$

Simplify the expression. Write your answer with positive exponents only. $6 ^ { 4 } \cdot 6 ^ { 7 }$

Multiply the polynomials by using the distributive property. $( 8 w + 7 ) ( w - 7 )$

Factor the polynomial by grouping (if possible). $2 x ^ { 5 } - 4 x ^ { 4 } + 4 x ^ { 3 } - 8 x ^ { 2 }$

Factor the function represented by f (x) and explain how the factored form relates to the graph of the function. $f ( x ) = x ^ { 2 } - 4 x - 21$

Write the number in standard notation. $8.6 \times 10 ^ { 6 }$

Factor out the greatest common factor. $30 t ^ { 2 } u + 12 t u ^ { 2 } + 24 t u$

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Exam 4: Polynomials

Factor completely. 125w3+127125 w ^ { 3 } + \frac { 1 } { 27 }125w3+271​

The height of a triangle is 2 feet more than 2 times the base. If the area is 42 ft2, find the base and height of the triangle.

Add the polynomials and simplify. (56w3+98w2−3.8w)+(−76w3−14w2−3.4w)\left( \frac { 5 } { 6 } w ^ { 3 } + \frac { 9 } { 8 } w ^ { 2 } - 3.8 w \right) + \left( - \frac { 7 } { 6 } w ^ { 3 } - \frac { 1 } { 4 } w ^ { 2 } - 3.4 w \right)(65​w3+89​w2−3.8w)+(−67​w3−41​w2−3.4w)

Multiply the expressions. [(4x+4)+y][(4x+4)−y][ ( 4 x + 4 ) + y ] [ ( 4 x + 4 ) - y ][(4x+4)+y][(4x+4)−y]

Determine which number is in "proper" scientific notation.

Divide the polynomials. −6x3+4x2−4x−2x\frac { - 6 x ^ { 3 } + 4 x ^ { 2 } - 4 x } { - 2 x }−2x−6x3+4x2−4x​

Simplify. 6−46 ^ { - 4 }6−4

Translate from algebraic form to English form. 9a39 a ^ { 3 }9a3

Factor the sum or difference of cubes. 27m3+125n327 m ^ { 3 } + 125 n ^ { 3 }27m3+125n3

Write the number in standard notation. 6.5×10−76.5 \times 10 ^ { - 7 }6.5×10−7

Solve the equation. r3=36rr ^ { 3 } = 36 rr3=36r

Factor out the greatest common factor. 20w3+70w220 w ^ { 3 } + 70 w ^ { 2 }20w3+70w2

Simplify the expression. Write your answer with positive exponents only. 64⋅676 ^ { 4 } \cdot 6 ^ { 7 }64⋅67

Multiply the polynomials by using the distributive property. (8w+7)(w−7)( 8 w + 7 ) ( w - 7 )(8w+7)(w−7)

Factor the polynomial by grouping (if possible). 2x5−4x4+4x3−8x22 x ^ { 5 } - 4 x ^ { 4 } + 4 x ^ { 3 } - 8 x ^ { 2 }2x5−4x4+4x3−8x2

Factor the function represented by f (x) and explain how the factored form relates to the graph of the function. f(x)=x2−4x−21f ( x ) = x ^ { 2 } - 4 x - 21f(x)=x2−4x−21

Write the number in standard notation. 8.6×1068.6 \times 10 ^ { 6 }8.6×106

Factor out the greatest common factor. 30t2u+12tu2+24tu30 t ^ { 2 } u + 12 t u ^ { 2 } + 24 t u30t2u+12tu2+24tu

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

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Factor completely. $125 w ^ { 3 } + \frac { 1 } { 27 }$

The height of a triangle is 2 feet more than 2 times the base. If the area is 42 ft², find the base and height of the triangle.

Add the polynomials and simplify. $\left( \frac { 5 } { 6 } w ^ { 3 } + \frac { 9 } { 8 } w ^ { 2 } - 3.8 w \right) + \left( - \frac { 7 } { 6 } w ^ { 3 } - \frac { 1 } { 4 } w ^ { 2 } - 3.4 w \right)$

Multiply the expressions. $[ ( 4 x + 4 ) + y ] [ ( 4 x + 4 ) - y ]$

Divide the polynomials. $\frac { - 6 x ^ { 3 } + 4 x ^ { 2 } - 4 x } { - 2 x }$

Simplify. $6 ^ { - 4 }$

Translate from algebraic form to English form. $9 a ^ { 3 }$

Factor the sum or difference of cubes. $27 m ^ { 3 } + 125 n ^ { 3 }$

Write the number in standard notation. $6.5 \times 10 ^ { - 7 }$

Solve the equation. $r ^ { 3 } = 36 r$

Factor out the greatest common factor. $20 w ^ { 3 } + 70 w ^ { 2 }$

Simplify the expression. Write your answer with positive exponents only. $6 ^ { 4 } \cdot 6 ^ { 7 }$

Multiply the polynomials by using the distributive property. $( 8 w + 7 ) ( w - 7 )$

Factor the polynomial by grouping (if possible). $2 x ^ { 5 } - 4 x ^ { 4 } + 4 x ^ { 3 } - 8 x ^ { 2 }$

Factor the function represented by f (x) and explain how the factored form relates to the graph of the function. $f ( x ) = x ^ { 2 } - 4 x - 21$

Write the number in standard notation. $8.6 \times 10 ^ { 6 }$

Factor out the greatest common factor. $30 t ^ { 2 } u + 12 t u ^ { 2 } + 24 t u$