Question 1

Multiply mentally.
-$\left(6 x^{4}-5\right)^{2}$

Accepted Answer

A)  $36 x^{8}-30 x^{4}+25$ 
B)  $36 x^{16}-60 x^{4}+25$ 
C)  $36 x^{8}-60 x^{4}+25$ 
D)  $36 x^{8}+25$ 
A)  $36 x^{8}-30 x^{4}+25$ 
B)  $36 x^{16}-60 x^{4}+25$ 
C)  $36 x^{8}-60 x^{4}+25$ 
D)  $36 x^{8}+25$

Question 2

Multiply.
-$(8 y-7)\left(64 y^{2}+56 y+49\right)$

Accepted Answer

A)  $512 y^{3}-343$ 
B)  $512 y^{3}+392 y^{2}-343$ 
C)  $64 y^{3}+343$ 
D)  $512 \mathrm{y}^{3}+343$ 
A)  $512 y^{3}-343$ 
B)  $512 y^{3}+392 y^{2}-343$ 
C)  $64 y^{3}+343$ 
D)  $512 \mathrm{y}^{3}+343$

Question 3

Simplify.
-$\left(\frac{b^{5}}{2}\right)^{-2}$

Accepted Answer

A)  $\frac{4}{b^{10}}$ 
B)  $\frac{b^{-10}}{2}$ 
C)  $\frac{b^{-7}}{2^{-2}}$ 
D)  $\frac{b^{10}}{2^{2}}$ 
A)  $\frac{4}{b^{10}}$ 
B)  $\frac{b^{-10}}{2}$ 
C)  $\frac{b^{-7}}{2^{-2}}$ 
D)  $\frac{b^{10}}{2^{2}}$

Question 4

Evaluate the polynomial.
-$x^{2}-4 y^{2}-x y$ for $x=3$ and $y=-3$

Accepted Answer

A)  36 
B)  -18 
C)  -36 
D)  54 
A)  36 
B)  -18 
C)  -36 
D)  54

Question 5

Divide.
-$\frac{20 x^{8}+60 x^{2}+50 x}{10 x}$

Accepted Answer

A)  $2 x^{7}+6 x+5$ 
B)  $2 x^{8}+60 x^{2}+50 x$ 
C)  $20 x^{7}+60 x+50$ 
D)  $2 x^{8}+6 x^{2}+5 x$ 
A)  $2 x^{7}+6 x+5$ 
B)  $2 x^{8}+60 x^{2}+50 x$ 
C)  $20 x^{7}+60 x+50$ 
D)  $2 x^{8}+6 x^{2}+5 x$

Question 6

Multiply.
-$(4 \mathrm{x}-11)(4 \mathrm{x}-11)$

Accepted Answer

A)  $4 x^{2}-88 x-89$ 
B)  $16 x^{2}+121 x-88$ 
C)  $16 x^{2}-88 x+121$ 
D)  $4 x^{2}-89 x+121$ 
A)  $4 x^{2}-88 x-89$ 
B)  $16 x^{2}+121 x-88$ 
C)  $16 x^{2}-88 x+121$ 
D)  $4 x^{2}-89 x+121$

Question 7

Multiply or divide and write scientific notation for the result.
-$\left(6 \times 10^{9}\right)\left(8 \times 10^{6}\right)$

Accepted Answer

A)  $48 \times 10^{16}$ 
B)  $4.8 \times 10^{16}$ 
C)  $4.8 \times 10^{15}$ 
D)  $48 \times 10^{54}$ 
A)  $48 \times 10^{16}$ 
B)  $4.8 \times 10^{16}$ 
C)  $4.8 \times 10^{15}$ 
D)  $48 \times 10^{54}$

Question 8

Solve the problem.
-Find a polynomial for the perimeter of the figure.

Accepted Answer

A)  $45 \mathrm{a}$ 
B)  $35 \mathrm{a}+12$ 
C)  $35 \mathrm{a}+10$ 
D)  45 
A)  $45 \mathrm{a}$ 
B)  $35 \mathrm{a}+12$ 
C)  $35 \mathrm{a}+10$ 
D)  45

Question 9

Divide.
-$\frac{9 x^{3} y^{3}+6 x^{5} y^{7}-9 x^{6} y^{4}}{3 x^{3} y^{3}}$

Accepted Answer

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

Question 10

Perform the division.
-$\frac{\mathrm{x}^{4}-16}{\mathrm{x}^{2}-4}$

Accepted Answer

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

Question 11

Solve the problem.
-The height $\mathrm{H}$ (in feet) of a ball thrown into the air from the top of a building after $t$ seconds is given by $\mathrm{H}=-16 \mathrm{t}^{2}+56 \mathrm{t}+211$. Use the graph below to estimate the height of the ball after 4.5 seconds.

Accepted Answer

A)  100 feet 
B)  140 feet 
C)  240 feet 
D)  $180 \mathrm{feet}$ 
A)  100 feet 
B)  140 feet 
C)  240 feet 
D)  $180 \mathrm{feet}$

Question 12

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-The national debt of a country is $\$ 53,100,000,000$ and the population is $5,900,000$. What is the debt per person? Write answer without exponents.

Accepted Answer

A)  $\$ 900$ 
B)  $\$ 313,290,000$ 
C)  $\$ 9000$ 
D)  $\$ 90,000$ 
A)  $\$ 900$ 
B)  $\$ 313,290,000$ 
C)  $\$ 9000$ 
D)  $\$ 90,000$

Question 13

Add.
-

Accepted Answer

A)  $1.13 \mathrm{x}^{4}-1.16 \mathrm{x}^{3}+0.32 \mathrm{x}^{2}+0.49 \mathrm{x}-0.85$ 
B)  $1.13 x^{12}-2.16 x^{9}-0.68 x^{4}+0.49 x-0.85$ 
C)  $1.13 \mathrm{x}^{4}-2.74 \mathrm{x}^{3}-0.68 \mathrm{x}^{2}+1.91 \mathrm{x}-0.85$ 
D)  $1.13 x^{4}-2.16 x^{3}-0.68 x^{2}+0.49 x-0.85$ 
A)  $1.13 \mathrm{x}^{4}-1.16 \mathrm{x}^{3}+0.32 \mathrm{x}^{2}+0.49 \mathrm{x}-0.85$ 
B)  $1.13 x^{12}-2.16 x^{9}-0.68 x^{4}+0.49 x-0.85$ 
C)  $1.13 \mathrm{x}^{4}-2.74 \mathrm{x}^{3}-0.68 \mathrm{x}^{2}+1.91 \mathrm{x}-0.85$ 
D)  $1.13 x^{4}-2.16 x^{3}-0.68 x^{2}+0.49 x-0.85$

Question 14

Collect like terms.
-$3 x^{7}-\frac{1}{2} x+3 x^{5}+\frac{1}{4} x+7 x^{7}$

Accepted Answer

A)  $10 x^{7}+3 x^{5}+\frac{1}{4} x$ 
B)  $13 \mathrm{x}^{19}-\frac{1}{4} \mathrm{x}$ 
C)  $13 x^{5}+\frac{1}{4} x$ 
D)  $10 x^{7}+3 x^{5}-\frac{1}{4} x$ 
A)  $10 x^{7}+3 x^{5}+\frac{1}{4} x$ 
B)  $13 \mathrm{x}^{19}-\frac{1}{4} \mathrm{x}$ 
C)  $13 x^{5}+\frac{1}{4} x$ 
D)  $10 x^{7}+3 x^{5}-\frac{1}{4} x$

Question 15

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-Assume that the volume of the earth is $5 \times 10^{14}$ cubic meters and the volume of a bacterium is $2.5 \times 10^{-16}$ cubic meters. If the earth could be filled with bacteria, how many would it contain?

Accepted Answer

A)  $2.0 \times 10^{30}$ bacteria 
B)  $2.0 \times 10^{-30}$ bacteria 
C)  $5.0 \times 10^{31}$ bacteria 
D)  $5.0 \times 10^{-31}$ bacteria 
A)  $2.0 \times 10^{30}$ bacteria 
B)  $2.0 \times 10^{-30}$ bacteria 
C)  $5.0 \times 10^{31}$ bacteria 
D)  $5.0 \times 10^{-31}$ bacteria

Question 16

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
-$-17 x^{4}+8 w^{3}-5 w-5 w^{5}+3$

Accepted Answer

A)  Trinomial, degree 13 
B)  Trinomial, degree 5 
C)  None, degree 5 
D)  Binomial, degree 14 
A)  Trinomial, degree 13 
B)  Trinomial, degree 5 
C)  None, degree 5 
D)  Binomial, degree 14

Question 17

Add.
-$6 x^{4}-9 x^{2}$
$\underline{7 x^{4}-9 x^{2}}$

Accepted Answer

A)  $13 x^{8}-18 x^{4}$ 
B)  $13 x^{4}-18 x^{2}$ 
C)  $-5 x^{6}$ 
D)  $-5 x^{12}$ 
A)  $13 x^{8}-18 x^{4}$ 
B)  $13 x^{4}-18 x^{2}$ 
C)  $-5 x^{6}$ 
D)  $-5 x^{12}$

Question 18

Identify the coefficient of each term of the polynomial.
-$-9 \mathrm{x}$

Accepted Answer

A)  9 
B)  $9 \mathrm{x}$ 
C)  -9 
D)  $-9 \mathrm{x}$ 
A)  9 
B)  $9 \mathrm{x}$ 
C)  -9 
D)  $-9 \mathrm{x}$

Question 19

Collect like terms.
-$\frac{1}{7} \mathrm{x}^{3}-\mathrm{x}+10+\frac{7}{6} \mathrm{x}^{3}+5 \mathrm{x}-9$

Accepted Answer

A)  $\frac{8}{13} x^{3}+4 x+1$ 
B)  $\frac{55}{42} x^{3}+6 x+1$ 
C)  $\frac{55}{42} x^{3}+4 x+19$ 
D)  $\frac{55}{42} x^{3}+4 x+1$ 
A)  $\frac{8}{13} x^{3}+4 x+1$ 
B)  $\frac{55}{42} x^{3}+6 x+1$ 
C)  $\frac{55}{42} x^{3}+4 x+19$ 
D)  $\frac{55}{42} x^{3}+4 x+1$

Question 20

Multiply.
-$\left(4 y^{2}-5 y-3\right)\left(y^{2}-3 y+5\right)$

Accepted Answer

A)  $4 y^{4}-12 y^{3}+35 y^{2}-16 y-15$ 
B)  $4 y^{4}-17 y^{3}+35 y^{2}-16 y-15$ 
C)  $4 y^{4}-12 y^{3}+32 y^{2}-16 y-15$ 
D)  $4 y^{4}-17 y^{3}+32 y^{2}-16 y-15$ 
A)  $4 y^{4}-12 y^{3}+35 y^{2}-16 y-15$ 
B)  $4 y^{4}-17 y^{3}+35 y^{2}-16 y-15$ 
C)  $4 y^{4}-12 y^{3}+32 y^{2}-16 y-15$ 
D)  $4 y^{4}-17 y^{3}+32 y^{2}-16 y-15$

Multiply mentally. - $\left(6 x^{4}-5\right)^{2}$

Multiply. - $(8 y-7)\left(64 y^{2}+56 y+49\right)$

Simplify. - $\left(\frac{b^{5}}{2}\right)^{-2}$

Evaluate the polynomial. - $x^{2}-4 y^{2}-x y$ for $x=3$ and $y=-3$

Divide. - $\frac{20 x^{8}+60 x^{2}+50 x}{10 x}$

Multiply. - $(4 \mathrm{x}-11)(4 \mathrm{x}-11)$

Multiply or divide and write scientific notation for the result. - $\left(6 \times 10^{9}\right)\left(8 \times 10^{6}\right)$

Solve the problem. -Find a polynomial for the perimeter of the figure.

Divide. - $\frac{9 x^{3} y^{3}+6 x^{5} y^{7}-9 x^{6} y^{4}}{3 x^{3} y^{3}}$

Perform the division. - $\frac{\mathrm{x}^{4}-16}{\mathrm{x}^{2}-4}$

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -The national debt of a country is $\$ 53,100,000,000$ and the population is $5,900,000$ . What is the debt per person? Write answer without exponents.

Add. -

Collect like terms. - $3 x^{7}-\frac{1}{2} x+3 x^{5}+\frac{1}{4} x+7 x^{7}$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - $-17 x^{4}+8 w^{3}-5 w-5 w^{5}+3$

Add. - $6 x^{4}-9 x^{2}$ $\underline{7 x^{4}-9 x^{2}}$

Identify the coefficient of each term of the polynomial. - $-9 \mathrm{x}$

Collect like terms. - $\frac{1}{7} \mathrm{x}^{3}-\mathrm{x}+10+\frac{7}{6} \mathrm{x}^{3}+5 \mathrm{x}-9$

Multiply. - $\left(4 y^{2}-5 y-3\right)\left(y^{2}-3 y+5\right)$

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

Multiply mentally. - (6x4−5)2\left(6 x^{4}-5\right)^{2}(6x4−5)2

Multiply. - (8y−7)(64y2+56y+49)(8 y-7)\left(64 y^{2}+56 y+49\right)(8y−7)(64y2+56y+49)

Simplify. - (b52)−2\left(\frac{b^{5}}{2}\right)^{-2}(2b5​)−2

Evaluate the polynomial. - x2−4y2−xyx^{2}-4 y^{2}-x yx2−4y2−xy for x=3x=3x=3 and y=−3y=-3y=−3

Divide. - 20x8+60x2+50x10x\frac{20 x^{8}+60 x^{2}+50 x}{10 x}10x20x8+60x2+50x​

Multiply. - (4x−11)(4x−11)(4 \mathrm{x}-11)(4 \mathrm{x}-11)(4x−11)(4x−11)

Multiply or divide and write scientific notation for the result. - (6×109)(8×106)\left(6 \times 10^{9}\right)\left(8 \times 10^{6}\right)(6×109)(8×106)