Question 1

Multiply and simplify.
-$(3 x)^{3}(3 x)^{4}$

Accepted Answer

A)  $(3 x)^{12}$ 
B)  $3 x^{7}$ 
C)  $(3 x)^{7}$ 
D)  $3 x^{12}$ 
A)  $(3 x)^{12}$ 
B)  $3 x^{7}$ 
C)  $(3 x)^{7}$ 
D)  $3 x^{12}$

Question 2

Multiply.
-$\left(3 x^{2}-7 x\right)\left(3 x^{2}+7 x\right)$

Accepted Answer

A)  $9 x^{4}-42 x^{3}-49 x^{2}$ 
B)  $9 x^{4}-49 x^{2}$ 
C)  $9 x^{4}+42 x^{3}-49 x^{2}$ 
D)  $3 x^{4}-7 x^{2}$ 
A)  $9 x^{4}-42 x^{3}-49 x^{2}$ 
B)  $9 x^{4}-49 x^{2}$ 
C)  $9 x^{4}+42 x^{3}-49 x^{2}$ 
D)  $3 x^{4}-7 x^{2}$

Question 3

Multiply.
-$(x-7)(x+7)$

Accepted Answer

A)  $x^{2}+14 x-49$ 
B)  $x^{2}-14$ 
C)  $x^{2}-14 x-49$ 
D)  $x^{2}-49$ 
A)  $x^{2}+14 x-49$ 
B)  $x^{2}-14$ 
C)  $x^{2}-14 x-49$ 
D)  $x^{2}-49$

Question 4

Express using positive exponents. Then simplify.
-$\left(\frac{1}{2}\right)^{-2}$

Accepted Answer

A)  $-\frac{1}{4}$ 
B)  $\frac{1}{4}$ 
C)  4 
D)  -4 
A)  $-\frac{1}{4}$ 
B)  $\frac{1}{4}$ 
C)  4 
D)  -4

Question 5

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
-$-16 y^{3}+9 y^{2}-3$

Accepted Answer

A)  Trinomial, degree 5 
B)  Trinomial, degree 6 
C)  Binomial, degree 3 
D)  Trinomial, degree 3 
A)  Trinomial, degree 5 
B)  Trinomial, degree 6 
C)  Binomial, degree 3 
D)  Trinomial, degree 3

Question 6

What is the meaning of the expression?
-$3 x^{3}$

Accepted Answer

A)  $3 \cdot 3 \cdot 3 \cdot x$ 
B)  $3 x \cdot 3 x \cdot 3 x$ 
C)  $3 \cdot x \cdot 3$ 
D)  $3 \cdot x \cdot x \cdot x$ 
A)  $3 \cdot 3 \cdot 3 \cdot x$ 
B)  $3 x \cdot 3 x \cdot 3 x$ 
C)  $3 \cdot x \cdot 3$ 
D)  $3 \cdot x \cdot x \cdot x$

Question 7

Write the number in scientific notation.
-58

Accepted Answer

A)  $5.8 \times 10^{-1}$ 
B)  $5.8 \times 10^{-2}$ 
C)  $5.8 \times 10^{2}$ 
D)  $5.8 \times 10^{1}$ 
A)  $5.8 \times 10^{-1}$ 
B)  $5.8 \times 10^{-2}$ 
C)  $5.8 \times 10^{2}$ 
D)  $5.8 \times 10^{1}$

Question 8

Solve the problem.
-During the first seconds, the height $h$ in feet of a baseball after $t$ seconds is given by $h=-16 t^{2}+81 t$ +3.1 . Use the graph below to estimate the height of the ball after 2 seconds.

Accepted Answer

A)  -64 feet 
B)  93 feet 
C)  117 feet 
D)  101 feet 
A)  -64 feet 
B)  93 feet 
C)  117 feet 
D)  101 feet

Question 9

Multiply.
-$(7 p-6)(7 p+6)$

Accepted Answer

A)  $p^{2}-36$ 
B)  $49 p^{2}-84 p-36$ 
C)  $49 p^{2}-36$ 
D)  $49 p^{2}+84 p-36$ 
A)  $p^{2}-36$ 
B)  $49 p^{2}-84 p-36$ 
C)  $49 p^{2}-36$ 
D)  $49 p^{2}+84 p-36$

Question 10

Evaluate.
-$a^{1}$

Accepted Answer

A)  1 
B)  - 1 
C)  $a$ 
D)  0 
A)  1 
B)  - 1 
C)  $a$ 
D)  0

Question 11

Evaluate.
-$\left(\frac{2}{5}\right)^{1}$

Accepted Answer

A)  $\frac{2}{5}$ 
B)  $\frac{5}{2}$ 
C)  $-\frac{2}{5}$ 
D)  1 
A)  $\frac{2}{5}$ 
B)  $\frac{5}{2}$ 
C)  $-\frac{2}{5}$ 
D)  1

Question 12

Multiply and simplify.
-$x \cdot x^{-8}$

Accepted Answer

A)  $x^{9}$ 
B)  $\frac{1}{x^{9}}$ 
C)  $x^{7}$ 
D)  $\frac{1}{x^{7}}$ 
A)  $x^{9}$ 
B)  $\frac{1}{x^{9}}$ 
C)  $x^{7}$ 
D)  $\frac{1}{x^{7}}$

Question 13

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

Accepted Answer

A)  4 
B)  40 
C)  -14 
D)  22 
A)  4 
B)  40 
C)  -14 
D)  22

Question 14

Write the number in scientific notation.
-0.000097614

Accepted Answer

A)  $9.7614 \times 10^{5}$ 
B)  $9.7614 \times 10^{-5}$ 
C)  $9.7614 \times 10^{4}$ 
D)  $9.7614 \times 10^{-4}$ 
A)  $9.7614 \times 10^{5}$ 
B)  $9.7614 \times 10^{-5}$ 
C)  $9.7614 \times 10^{4}$ 
D)  $9.7614 \times 10^{-4}$

Question 15

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-A computer can do one calculation in $1.4 \times 10^{-7}$ seconds.

Accepted Answer

A)  $14,000,000$ 
B)  0.00000014 
C)  0.000014 
D)  0.000000014 
A)  $14,000,000$ 
B)  0.00000014 
C)  0.000014 
D)  0.000000014

Question 16

Collect like terms.
-$2 z^{4}-11 z+5 z^{4}-5$

Accepted Answer

A)  $7 z^{4}-11 z-5$ 
B)  $-9 z^{4}$ 
C)  $-110 z^{4}-5$ 
D)  $-4 z^{4}-5$ 
A)  $7 z^{4}-11 z-5$ 
B)  $-9 z^{4}$ 
C)  $-110 z^{4}-5$ 
D)  $-4 z^{4}-5$

Question 17

Convert to decimal notation.
-$10^{-2}$

Accepted Answer

A)  1 
B)  0.1 
C)  0.001 
D)  0.01 
A)  1 
B)  0.1 
C)  0.001 
D)  0.01

Question 18

Divide and simplify.
-$\frac{(3 p)^{12}}{(3 p)^{8}}$

Accepted Answer

A)  $81 p^{4}$ 
B)  $\frac{p^{4}}{81}$ 
C)  $\frac{81}{\mathrm{p}^{4}}$ 
D)  $\frac{1}{81 p^{4}}$ 
A)  $81 p^{4}$ 
B)  $\frac{p^{4}}{81}$ 
C)  $\frac{81}{\mathrm{p}^{4}}$ 
D)  $\frac{1}{81 p^{4}}$

Question 19

Divide and simplify.
-$\frac{\mathrm{z}^{-7}}{\mathrm{z}^{-5}}$

Accepted Answer

A)  $\frac{1}{z^{-2}}$ 
B)  $\mathrm{z}^{2}$ 
C)  $\frac{1}{z^{2}}$ 
D)  $z^{12}$ 
A)  $\frac{1}{z^{-2}}$ 
B)  $\mathrm{z}^{2}$ 
C)  $\frac{1}{z^{2}}$ 
D)  $z^{12}$

Question 20

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 $\mathrm{H}=-16 \mathrm{t}^{2}+70 \mathrm{t}+226$. Use the graph below to find the approximate value of $-16 \mathrm{t}^{2}+70 \mathrm{t}+226$ for $\mathrm{x}=1$.

Accepted Answer

A)  380 feet 
B)  280 feet 
C)  240 feet 
D)  320 feet 
A)  380 feet 
B)  280 feet 
C)  240 feet 
D)  320 feet

Multiply and simplify. - $(3 x)^{3}(3 x)^{4}$

Multiply. - $\left(3 x^{2}-7 x\right)\left(3 x^{2}+7 x\right)$

Multiply. - $(x-7)(x+7)$

Express using positive exponents. Then simplify. - $\left(\frac{1}{2}\right)^{-2}$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - $-16 y^{3}+9 y^{2}-3$

What is the meaning of the expression? - $3 x^{3}$

Write the number in scientific notation. -58

Multiply. - $(7 p-6)(7 p+6)$

Evaluate. - $a^{1}$

Evaluate. - $\left(\frac{2}{5}\right)^{1}$

Multiply and simplify. - $x \cdot x^{-8}$

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

Write the number in scientific notation. -0.000097614

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -A computer can do one calculation in $1.4 \times 10^{-7}$ seconds.

Collect like terms. - $2 z^{4}-11 z+5 z^{4}-5$

Convert to decimal notation. - $10^{-2}$

Divide and simplify. - $\frac{(3 p)^{12}}{(3 p)^{8}}$

Divide and simplify. - $\frac{\mathrm{z}^{-7}}{\mathrm{z}^{-5}}$

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 and simplify. - (3x)3(3x)4(3 x)^{3}(3 x)^{4}(3x)3(3x)4

Multiply. - (3x2−7x)(3x2+7x)\left(3 x^{2}-7 x\right)\left(3 x^{2}+7 x\right)(3x2−7x)(3x2+7x)

Multiply. - (x−7)(x+7)(x-7)(x+7)(x−7)(x+7)

Express using positive exponents. Then simplify. - (12)−2\left(\frac{1}{2}\right)^{-2}(21​)−2

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - −16y3+9y2−3-16 y^{3}+9 y^{2}-3−16y3+9y2−3

What is the meaning of the expression? - 3x33 x^{3}3x3