Question 1

Simplify.
-Add $4 x ^ { 2 } y - 7 x y + 3$ and $- 3 x ^ { 2 } y + 10 x y - 8$

Accepted Answer

A)  $- x ^ { 2 } y - 17 x y + 11$ 
B)  $7 x ^ { 2 } y + 17 x y + 11$ 
C)  $x ^ { 2 } y + 3 x y - 5$ 
D)  $3 x ^ { 3 } y ^ { 2 } - 5$ 
A)  $- x ^ { 2 } y - 17 x y + 11$ 
B)  $7 x ^ { 2 } y + 17 x y + 11$ 
C)  $x ^ { 2 } y + 3 x y - 5$ 
D)  $3 x ^ { 3 } y ^ { 2 } - 5$

Question 2

Solve the problem.
-The area of a circle of radius r is given by the polynomialal $$\pi r ^ { 2 },$$ , where π is an irrational number. Use 3.14 as an approximation of $\pi ,$ and find the area of a circle with radius 7 cm.

Accepted Answer

A)  $147 \mathrm {~cm} ^ { 2 }$ 
B)  $21.98 \mathrm {~cm} ^ { 2 }$ 
C)  $153.86 \mathrm {~cm} ^ { 2 }$ 
D)  $43.96 \mathrm {~cm} ^ { 2 }$ 
A)  $147 \mathrm {~cm} ^ { 2 }$ 
B)  $21.98 \mathrm {~cm} ^ { 2 }$ 
C)  $153.86 \mathrm {~cm} ^ { 2 }$ 
D)  $43.96 \mathrm {~cm} ^ { 2 }$

Question 3

Simplify.
-$\left( - \frac { 10 } { 11 } x ^ { 2 } y + \frac { 2 } { 3 } \right) - \left( - \frac { 2 } { 11 } x ^ { 2 } y - \frac { 1 } { 6 } \right)$

Accepted Answer

A)  $\frac { 8 } { 11 } x ^ { 2 } y + \frac { 5 } { 6 }$ 
B)  $- \frac { 8 } { 11 } x ^ { 2 } y + \frac { 5 } { 6 }$ 
C)  $\frac { 8 } { 11 } x ^ { 2 } y + \frac { 1 } { 2 }$ 
D)  $- \frac { 8 } { 11 } x ^ { 2 } y + \frac { 1 } { 2 }$ 
A)  $\frac { 8 } { 11 } x ^ { 2 } y + \frac { 5 } { 6 }$ 
B)  $- \frac { 8 } { 11 } x ^ { 2 } y + \frac { 5 } { 6 }$ 
C)  $\frac { 8 } { 11 } x ^ { 2 } y + \frac { 1 } { 2 }$ 
D)  $- \frac { 8 } { 11 } x ^ { 2 } y + \frac { 1 } { 2 }$

Question 4

Multiply.
-$3 m n \left( 4 m ^ { 2 } - 3 m n + 4 n ^ { 2 } \right)$

Accepted Answer

A)  $12 m ^ { 3 } n + 9 m ^ { 2 } n ^ { 2 } + 12 m n ^ { 3 }$ 
B)  $12 m ^ { 3 } n - 3 m n + 4 n ^ { 2 }$ 
C)  $12 m ^ { 3 } n - 9 m ^ { 2 } n ^ { 2 } + 12 m n ^ { 3 }$ 
D)  $12 m ^ { 2 } n - 9 m n + 12 m n ^ { 2 }$ 
A)  $12 m ^ { 3 } n + 9 m ^ { 2 } n ^ { 2 } + 12 m n ^ { 3 }$ 
B)  $12 m ^ { 3 } n - 3 m n + 4 n ^ { 2 }$ 
C)  $12 m ^ { 3 } n - 9 m ^ { 2 } n ^ { 2 } + 12 m n ^ { 3 }$ 
D)  $12 m ^ { 2 } n - 9 m n + 12 m n ^ { 2 }$

Question 5

Give the degree of the polynomial and identify its leading coefficient.
-$3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s$

Accepted Answer

A) degree: 5; leading coefficient: 3 
B) degree: 4; leading coefficient: 1 
C) degree: 5; leading coefficient: 15 
D) degree: 4; leading coefficient: 3 
A) degree: 5; leading coefficient: 3 
B) degree: 4; leading coefficient: 1 
C) degree: 5; leading coefficient: 15 
D) degree: 4; leading coefficient: 3

Question 6

Solve the problem.
-The position of an object moving in a straight line is given by $\mathrm { s } = 11 \mathrm { t } ^ { 2 } - 7 \mathrm { t },$ where s is in where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 15 seconds?

Accepted Answer

A) 1410 meters 
B) 60 meters 
C) 900 meters 
D) 2370 meters 
A) 1410 meters 
B) 60 meters 
C) 900 meters 
D) 2370 meters

Question 7

Simplify.
-$( 3 a - 2 b - 5 c ) - ( 9 a - 6 b - 7 c )$

Accepted Answer

A)  $12 a - 8 b - 12 c$ 
B)  $- 6 a - 8 b + 2 c$ 
C)  $- 6 a + 4 b + 2 c$ 
D)  $- 6 a + 4 b - 12 c$ 
A)  $12 a - 8 b - 12 c$ 
B)  $- 6 a - 8 b + 2 c$ 
C)  $- 6 a + 4 b + 2 c$ 
D)  $- 6 a + 4 b - 12 c$

Question 8

Simplify. Assume that all exponents represent natural numbers.
-$\left( 8 x ^ { 2 r } - x ^ { r } - 1 \right) + \left( x ^ { 2 r } + 5 x ^ { r } + 3 \right)$

Accepted Answer

A)  $9 x ^ { 4 r } + 6 x ^ { 2 r } + 4$ 
B)  $7 x ^ { 4 r } - 6 x ^ { 2 r } - 4$ 
C)  $9 x ^ { 2 r } + 4 x ^ { r } + 2$ 
D)  $8 x ^ { 2 r } + 5 x ^ { r } + 3$ 
A)  $9 x ^ { 4 r } + 6 x ^ { 2 r } + 4$ 
B)  $7 x ^ { 4 r } - 6 x ^ { 2 r } - 4$ 
C)  $9 x ^ { 2 r } + 4 x ^ { r } + 2$ 
D)  $8 x ^ { 2 r } + 5 x ^ { r } + 3$

Question 9

Simplify.
-$\left( 2.5 x ^ { 3 } - 5.2 x ^ { 2 } - 4 \right) - \left( 8.8 x ^ { 3 } - 3.2 x ^ { 2 } + 3 \right)$

Accepted Answer

A)  $- 6.3 x ^ { 3 } - 2 x ^ { 2 } - 7$ 
B)  $11.3 x ^ { 3 } - 2 x ^ { 2 } - 7$ 
C)  $- 6.3 x ^ { 3 } - 2 x ^ { 2 } + 7$ 
D)  $- 6.3 x ^ { 3 } - 8.4 x ^ { 2 } - 7$ 
A)  $- 6.3 x ^ { 3 } - 2 x ^ { 2 } - 7$ 
B)  $11.3 x ^ { 3 } - 2 x ^ { 2 } - 7$ 
C)  $- 6.3 x ^ { 3 } - 2 x ^ { 2 } + 7$ 
D)  $- 6.3 x ^ { 3 } - 8.4 x ^ { 2 } - 7$

Question 10

Simplify.
-$\left( 5 m + 10 m ^ { 3 } \right) - \left( - 8 - 3 m - 3 m ^ { 3 } \right)$

Accepted Answer

A)  $13 m ^ { 3 } + 8 m + 8$ 
B)  $$7 m ^ { 3 } + 8 m - 8$$ 
C)  $7 m ^ { 3 } + 8 m + 8$ 
D)  $13 m ^ { 3 } + 8 m - 8$ 
A)  $13 m ^ { 3 } + 8 m + 8$ 
B)  $$7 m ^ { 3 } + 8 m - 8$$ 
C)  $7 m ^ { 3 } + 8 m + 8$ 
D)  $13 m ^ { 3 } + 8 m - 8$

Question 11

Determine which of the graphs is the graph of the equation.
-$f ( x ) = - 3 x ^ { 2 } + 3 x + 2$

Accepted Answer

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

Question 12

Multiply. Assume that all variables represent natural numbers.
-$7 x ^ { 2 } y ^ { n } \left( - 9 x y ^ { n + 1 } + 11 \right)$

Accepted Answer

A)  $- 63 x ^ { 2 } y ^ { 2 n + 1 } + 77 x ^ { 2 } y ^ { n }$ 
B)  $- 63 x ^ { 3 } y ^ { 2 n + 1 } + 77 x ^ { 2 } y ^ { n }$ 
C)  $- 63 x ^ { 3 } y ^ { n ^ { 2 } + 1 } + 77 x ^ { 2 } y ^ { n }$ 
D)  $- 63 x ^ { 3 } y ^ { 2 n } + 77 x ^ { 2 } y ^ { n }$ 
A)  $- 63 x ^ { 2 } y ^ { 2 n + 1 } + 77 x ^ { 2 } y ^ { n }$ 
B)  $- 63 x ^ { 3 } y ^ { 2 n + 1 } + 77 x ^ { 2 } y ^ { n }$ 
C)  $- 63 x ^ { 3 } y ^ { n ^ { 2 } + 1 } + 77 x ^ { 2 } y ^ { n }$ 
D)  $- 63 x ^ { 3 } y ^ { 2 n } + 77 x ^ { 2 } y ^ { n }$

Simplify. -Add $4 x ^ { 2 } y - 7 x y + 3$ and $- 3 x ^ { 2 } y + 10 x y - 8$

Solve the problem. -The area of a circle of radius r is given by the polynomialal $\pi r ^ { 2 },$ , where π is an irrational number. Use 3.14 as an approximation of $\pi ,$ and find the area of a circle with radius 7 cm.

Simplify. - $\left( - \frac { 10 } { 11 } x ^ { 2 } y + \frac { 2 } { 3 } \right) - \left( - \frac { 2 } { 11 } x ^ { 2 } y - \frac { 1 } { 6 } \right)$

Multiply. - $3 m n \left( 4 m ^ { 2 } - 3 m n + 4 n ^ { 2 } \right)$

Give the degree of the polynomial and identify its leading coefficient. - $3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s$

Solve the problem. -The position of an object moving in a straight line is given by $\mathrm { s } = 11 \mathrm { t } ^ { 2 } - 7 \mathrm { t },$ where s is in where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 15 seconds?

Simplify. - $( 3 a - 2 b - 5 c ) - ( 9 a - 6 b - 7 c )$

Simplify. Assume that all exponents represent natural numbers. - $\left( 8 x ^ { 2 r } - x ^ { r } - 1 \right) + \left( x ^ { 2 r } + 5 x ^ { r } + 3 \right)$

Simplify. - $\left( 2.5 x ^ { 3 } - 5.2 x ^ { 2 } - 4 \right) - \left( 8.8 x ^ { 3 } - 3.2 x ^ { 2 } + 3 \right)$

Simplify. - $\left( 5 m + 10 m ^ { 3 } \right) - \left( - 8 - 3 m - 3 m ^ { 3 } \right)$

Determine which of the graphs is the graph of the equation. - $f ( x ) = - 3 x ^ { 2 } + 3 x + 2$

Multiply. Assume that all variables represent natural numbers. - $7 x ^ { 2 } y ^ { n } \left( - 9 x y ^ { n + 1 } + 11 \right)$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 5: Polynomials and Polynomial Functions

Simplify. -Add 4x2y−7xy+34 x ^ { 2 } y - 7 x y + 34x2y−7xy+3 and −3x2y+10xy−8- 3 x ^ { 2 } y + 10 x y - 8−3x2y+10xy−8

Solve the problem. -The area of a circle of radius r is given by the polynomialal πr2,\pi r ^ { 2 },πr2, , where π is an irrational number. Use 3.14 as an approximation of π,\pi ,π, and find the area of a circle with radius 7 cm.

Simplify. - (−1011x2y+23)−(−211x2y−16)\left( - \frac { 10 } { 11 } x ^ { 2 } y + \frac { 2 } { 3 } \right) - \left( - \frac { 2 } { 11 } x ^ { 2 } y - \frac { 1 } { 6 } \right)(−1110​x2y+32​)−(−112​x2y−61​)

Multiply. - 3mn(4m2−3mn+4n2)3 m n \left( 4 m ^ { 2 } - 3 m n + 4 n ^ { 2 } \right)3mn(4m2−3mn+4n2)

Give the degree of the polynomial and identify its leading coefficient. - 3q2r2+rs3+15qr3s3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s3q2r2+rs3+15qr3s

Simplify. - (3a−2b−5c)−(9a−6b−7c)( 3 a - 2 b - 5 c ) - ( 9 a - 6 b - 7 c )(3a−2b−5c)−(9a−6b−7c)

Simplify. Assume that all exponents represent natural numbers. - (8x2r−xr−1)+(x2r+5xr+3)\left( 8 x ^ { 2 r } - x ^ { r } - 1 \right) + \left( x ^ { 2 r } + 5 x ^ { r } + 3 \right)(8x2r−xr−1)+(x2r+5xr+3)

Simplify. - (2.5x3−5.2x2−4)−(8.8x3−3.2x2+3)\left( 2.5 x ^ { 3 } - 5.2 x ^ { 2 } - 4 \right) - \left( 8.8 x ^ { 3 } - 3.2 x ^ { 2 } + 3 \right)(2.5x3−5.2x2−4)−(8.8x3−3.2x2+3)

Simplify. - (5m+10m3)−(−8−3m−3m3)\left( 5 m + 10 m ^ { 3 } \right) - \left( - 8 - 3 m - 3 m ^ { 3 } \right)(5m+10m3)−(−8−3m−3m3)

Determine which of the graphs is the graph of the equation. - f(x)=−3x2+3x+2f ( x ) = - 3 x ^ { 2 } + 3 x + 2f(x)=−3x2+3x+2

Multiply. Assume that all variables represent natural numbers. - 7x2yn(−9xyn+1+11)7 x ^ { 2 } y ^ { n } \left( - 9 x y ^ { n + 1 } + 11 \right)7x2yn(−9xyn+1+11)