Question 1

Compute each expression and compare.
-$4^{2}+2^{2} ;(4+2)^{2}$

Accepted Answer

A)  12; 36; square of sum is greater than sum of squares 
B)  20; 12 ; sum of squares is greater than square of sum 
C)  20; 36; square of sum is greater than sum of squares 
D)  12; 12; both are equal 
A)  12; 36; square of sum is greater than sum of squares 
B)  20; 12 ; sum of squares is greater than square of sum 
C)  20; 36; square of sum is greater than sum of squares 
D)  12; 12; both are equal

Question 2

Multiply.
-$(x-1.9)(x+3.3)$

Accepted Answer

A)  $x^{2}-5.2 x-6.27$ 
B)  $x^{2}+1.4 x-6.27$ 
C)  $x^{2}+5.2 x-6.27$ 
D)  $x^{2}-1.4 x-6.27$ 
A)  $x^{2}-5.2 x-6.27$ 
B)  $x^{2}+1.4 x-6.27$ 
C)  $x^{2}+5.2 x-6.27$ 
D)  $x^{2}-1.4 x-6.27$

Question 3

Multiply mentally.
-$\left(4 x^{2}+7\right)\left(x^{2}-7\right)$

Accepted Answer

A)  $4 x^{2}-21 x-49$ 
B)  $4 x^{2}-22 x-49$ 
C)  $4 x^{4}-21 x^{2}-49$ 
D)  $4 x^{3}-28 x^{2}+7 x-49$ 
A)  $4 x^{2}-21 x-49$ 
B)  $4 x^{2}-22 x-49$ 
C)  $4 x^{4}-21 x^{2}-49$ 
D)  $4 x^{3}-28 x^{2}+7 x-49$

Question 4

Evaluate the polynomial.
-$8-\frac{1}{9} \mathrm{x}$, when $\mathrm{x}=0$

Accepted Answer

A)  0 
B)  8 
C)  -8 
D)  $-\frac{1}{9}$ 
A)  0 
B)  8 
C)  -8 
D)  $-\frac{1}{9}$

Question 5

Identify the missing terms in the polynomial.
-$x^{3}-16$

Accepted Answer

A)  $\mathrm{x}$ - term 
B)  $x^{2}$ - term, $x$ - term 
C)  $x^{4}$ - term, $x^{2}$ - term, $x$ - term 
D)  $x^{2}$ - term 
A)  $\mathrm{x}$ - term 
B)  $x^{2}$ - term, $x$ - term 
C)  $x^{4}$ - term, $x^{2}$ - term, $x$ - term 
D)  $x^{2}$ - term

Question 6

Perform the division.
-$\left(\mathrm{x}^{2}-49\right) \div(\mathrm{x}-7)$

Accepted Answer

A)  $x-49$ 
B)  $x^{2}-7$ 
C)  $x+49$ 
D)  $x+7$ 
A)  $x-49$ 
B)  $x^{2}-7$ 
C)  $x+49$ 
D)  $x+7$

Question 7

Evaluate the polynomial.
-$-\mathrm{xyz}$ for $\mathrm{x}=1, \mathrm{y}=-2$, and $\mathrm{z}=3$

Accepted Answer

A)  6 
B)  -6 
C)  1 
D)  81 
A)  6 
B)  -6 
C)  1 
D)  81

Question 8

Convert to decimal notation.
-$6.072 \times 10^{5}$

Accepted Answer

A)  $6,072,000$ 
B)  607,200 
C)  60,720 
D)  303.6 
A)  $6,072,000$ 
B)  607,200 
C)  60,720 
D)  303.6

Question 9

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

Accepted Answer

A)  $x^{4}+4 x^{3} y+3 x^{2} y^{2}+14 x y^{3}-5 y^{4}$ 
B)  $x^{4}+4 x^{3} y+9 x^{2} y^{2}+14 x y^{3}+5 y^{4}$ 
C)  $x^{4}+2 x^{3} y+3 x^{2} y^{2}+16 x y^{3}-5 y^{4}$ 
D)  $x^{4}+2 x^{3} y+3 x^{2} y^{2}+14 x y^{3}+5 y^{4}$ 
A)  $x^{4}+4 x^{3} y+3 x^{2} y^{2}+14 x y^{3}-5 y^{4}$ 
B)  $x^{4}+4 x^{3} y+9 x^{2} y^{2}+14 x y^{3}+5 y^{4}$ 
C)  $x^{4}+2 x^{3} y+3 x^{2} y^{2}+16 x y^{3}-5 y^{4}$ 
D)  $x^{4}+2 x^{3} y+3 x^{2} y^{2}+14 x y^{3}+5 y^{4}$

Question 10

Evaluate.
-$\left(-\frac{2}{7}\right)^{0}$

Accepted Answer

A)  0 
B)  - 1 
C)  $\frac{2}{7}$ 
D)  1 
A)  0 
B)  - 1 
C)  $\frac{2}{7}$ 
D)  1

Question 11

Express using positive exponents. Then simplify.
-$\frac{1}{x^{-m}}$

Accepted Answer

A)  $\frac{1}{x^{m}}$ 
B)  $x^{m}$ 
C)  $\mathrm{mx}$ 
D)  $x^{-m}$ 
A)  $\frac{1}{x^{m}}$ 
B)  $x^{m}$ 
C)  $\mathrm{mx}$ 
D)  $x^{-m}$

Question 12

Multiply.
-$(2 x-9)(2 x-9)$

Accepted Answer

A)  $2 x^{2}-37 x+81$ 
B)  $4 x^{2}-36 x+81$ 
C)  $4 x^{2}+81 x-36$ 
D)  $2 x^{2}-36 x-37$ 
A)  $2 x^{2}-37 x+81$ 
B)  $4 x^{2}-36 x+81$ 
C)  $4 x^{2}+81 x-36$ 
D)  $2 x^{2}-36 x-37$

Question 13

Express the following using negative exponents.
-$\frac{1}{\mathrm{x}^{9}}$

Accepted Answer

A)  $x^{9}$ 
B)  $9^{-x}$ 
C)  $x^{-9}$ 
D)  $9^{-x+1}$ 
A)  $x^{9}$ 
B)  $9^{-x}$ 
C)  $x^{-9}$ 
D)  $9^{-x+1}$

Question 14

Evaluate the polynomial.
-$x^{2} y z+x+y$ for $x=1, y=-4$, and $z=4$

Accepted Answer

A)  -19 
B)  7 
C)  10 
D)  -16 
A)  -19 
B)  7 
C)  10 
D)  -16

Question 15

Evaluate the polynomial.
-$2 x^{3}+5 x^{2}-x+17$, when $x=0$

Accepted Answer

A)  0 
B)  -27 
C)  -37 
D)  17 
A)  0 
B)  -27 
C)  -37 
D)  17

Question 16

Multiply.
-$(2 x+12)(2 x-12)$

Accepted Answer

A)  $4 x^{2}+48 x-144$ 
B)  $2 x^{2}-48 x-144$ 
C)  $4 x^{2}-48 x-144$ 
D)  $4 x^{2}-144$ 
A)  $4 x^{2}+48 x-144$ 
B)  $2 x^{2}-48 x-144$ 
C)  $4 x^{2}-48 x-144$ 
D)  $4 x^{2}-144$

Question 17

Write the number in scientific notation.
-$14,000,000$

Accepted Answer

A)  $1.4 \times 10^{6}$ 
B)  $1.4 \times 10^{-6}$ 
C)  $1.4 \times 10^{7}$ 
D)  $1.4 \times 10^{-7}$ 
A)  $1.4 \times 10^{6}$ 
B)  $1.4 \times 10^{-6}$ 
C)  $1.4 \times 10^{7}$ 
D)  $1.4 \times 10^{-7}$

Question 18

Evaluate the polynomial.
-$x^{2}+3 y^{2}+2 x y$ for $x=5$ and $y=3$

Accepted Answer

A)  82 
B)  52 
C)  97 
D)  55 
A)  82 
B)  52 
C)  97 
D)  55

Question 19

Multiply mentally.
-$\left(3 x^{2}-\frac{3}{5}\right)\left(3 x^{2}+\frac{3}{5}\right)$

Accepted Answer

A)  $9 x^{2}-30 x-\frac{9}{25}$ 
B)  $9 x^{2}+30 x-\frac{9}{25}$ 
C)  $9 x^{2}-\frac{9}{25}$ 
D)  $9 x^{4}-\frac{9}{25}$ 
A)  $9 x^{2}-30 x-\frac{9}{25}$ 
B)  $9 x^{2}+30 x-\frac{9}{25}$ 
C)  $9 x^{2}-\frac{9}{25}$ 
D)  $9 x^{4}-\frac{9}{25}$

Question 20

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-The earth is approximately $92,900,000$ miles from the sun. If 1 mile $=1.61 \times 10^{3} \mathrm{~m}$, what is the distance to the sun in meters?

Accepted Answer

A)  $1.50 \times 10^{10} \mathrm{~m}$ 
B)  $5.7 \times 10^{-10} \mathrm{~m}$ 
C)  $1.50 \times 10^{11} \mathrm{~m}$ 
D)  $5.7 \times 10^{10} \mathrm{~m}$ 
A)  $1.50 \times 10^{10} \mathrm{~m}$ 
B)  $5.7 \times 10^{-10} \mathrm{~m}$ 
C)  $1.50 \times 10^{11} \mathrm{~m}$ 
D)  $5.7 \times 10^{10} \mathrm{~m}$

Compute each expression and compare. - $4^{2}+2^{2} ;(4+2)^{2}$

Multiply. - $(x-1.9)(x+3.3)$

Multiply mentally. - $\left(4 x^{2}+7\right)\left(x^{2}-7\right)$

Evaluate the polynomial. - $8-\frac{1}{9} \mathrm{x}$ , when $\mathrm{x}=0$

Identify the missing terms in the polynomial. - $x^{3}-16$

Perform the division. - $\left(\mathrm{x}^{2}-49\right) \div(\mathrm{x}-7)$

Evaluate the polynomial. - $-\mathrm{xyz}$ for $\mathrm{x}=1, \mathrm{y}=-2$ , and $\mathrm{z}=3$

Convert to decimal notation. - $6.072 \times 10^{5}$

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

Evaluate. - $\left(-\frac{2}{7}\right)^{0}$

Express using positive exponents. Then simplify. - $\frac{1}{x^{-m}}$

Multiply. - $(2 x-9)(2 x-9)$

Express the following using negative exponents. - $\frac{1}{\mathrm{x}^{9}}$

Evaluate the polynomial. - $x^{2} y z+x+y$ for $x=1, y=-4$ , and $z=4$

Evaluate the polynomial. - $2 x^{3}+5 x^{2}-x+17$ , when $x=0$

Multiply. - $(2 x+12)(2 x-12)$

Write the number in scientific notation. - $14,000,000$

Evaluate the polynomial. - $x^{2}+3 y^{2}+2 x y$ for $x=5$ and $y=3$

Multiply mentally. - $\left(3 x^{2}-\frac{3}{5}\right)\left(3 x^{2}+\frac{3}{5}\right)$

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -The earth is approximately $92,900,000$ miles from the sun. If 1 mile $=1.61 \times 10^{3} \mathrm{~m}$ , what is the distance to the sun in meters?

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Factoring

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

Filters

Exam 4: Polynomials: Operations

Compute each expression and compare. - 42+22;(4+2)24^{2}+2^{2} ;(4+2)^{2}42+22;(4+2)2

Multiply. - (x−1.9)(x+3.3)(x-1.9)(x+3.3)(x−1.9)(x+3.3)

Multiply mentally. - (4x2+7)(x2−7)\left(4 x^{2}+7\right)\left(x^{2}-7\right)(4x2+7)(x2−7)

Evaluate the polynomial. - 8−19x8-\frac{1}{9} \mathrm{x}8−91​x , when x=0\mathrm{x}=0x=0

Identify the missing terms in the polynomial. - x3−16x^{3}-16x3−16

Perform the division. - (x2−49)÷(x−7)\left(\mathrm{x}^{2}-49\right) \div(\mathrm{x}-7)(x2−49)÷(x−7)

Evaluate the polynomial. - −xyz-\mathrm{xyz}−xyz for x=1,y=−2\mathrm{x}=1, \mathrm{y}=-2x=1,y=−2 , and z=3\mathrm{z}=3z=3

Convert to decimal notation. - 6.072×1056.072 \times 10^{5}6.072×105

Multiply. - (x2+5y2−xy)(x2+3xy+y2)\left(x^{2}+5 y^{2}-x y\right)\left(x^{2}+3 x y+y^{2}\right)(x2+5y2−xy)(x2+3xy+y2)

Evaluate. - (−27)0\left(-\frac{2}{7}\right)^{0}(−72​)0

Express using positive exponents. Then simplify. - 1x−m\frac{1}{x^{-m}}x−m1​

Multiply. - (2x−9)(2x−9)(2 x-9)(2 x-9)(2x−9)(2x−9)

Express the following using negative exponents. - 1x9\frac{1}{\mathrm{x}^{9}}x91​

Evaluate the polynomial. - x2yz+x+yx^{2} y z+x+yx2yz+x+y for x=1,y=−4x=1, y=-4x=1,y=−4 , and z=4z=4z=4

Evaluate the polynomial. - 2x3+5x2−x+172 x^{3}+5 x^{2}-x+172x3+5x2−x+17 , when x=0x=0x=0

Multiply. - (2x+12)(2x−12)(2 x+12)(2 x-12)(2x+12)(2x−12)

Write the number in scientific notation. - 14,000,00014,000,00014,000,000

Evaluate the polynomial. - x2+3y2+2xyx^{2}+3 y^{2}+2 x yx2+3y2+2xy for x=5x=5x=5 and y=3y=3y=3

Multiply mentally. - (3x2−35)(3x2+35)\left(3 x^{2}-\frac{3}{5}\right)\left(3 x^{2}+\frac{3}{5}\right)(3x2−53​)(3x2+53​)

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -The earth is approximately 92,900,00092,900,00092,900,000 miles from the sun. If 1 mile =1.61×103 m=1.61 \times 10^{3} \mathrm{~m}=1.61×103 m , what is the distance to the sun in meters?