Question 1

Perform the division.
-$\frac{-6 x^{3}-11 x^{2}+22 x-8}{3 x-2}$
A) $-2 x^{2}-5 x+4$
B) $x^{2}+5 x-4$
C) $-2 x^{2}+4$
D) $x^{2}-5 x+4$

Accepted Answer

The division $\frac{-6 x^{3}-11 x^{2}+22 x-8}{3 x-2}$ can be performed using polynomial long division or synthetic division. The result is $-2 x^{2}-5 x+4$, which matches option A.

Question 2

Perform the division.
-$\frac{-8 x^{3}+28 x^{2}-10 x-11}{2 x-5}$
A) $-4 x^{2}+4 x+5+\frac{17}{2 x-5}$
B) $-4 x^{2}+4 x+5$
C) $-4 x^{2}+4 x+5+\frac{14}{2 x-5}$
D) $x^{2}+5+\frac{4}{2 x-5}$

Accepted Answer

The answer of Perform the division.
-$\frac{-8 x^{3}+28 x^{2}-10 x-11}{2 x-5}$
A)...

Question 3

Provide an appropriate response.
- $\left(\frac{\mathrm{r}}{\mathrm{s}}\right)^{3}=\frac{\mathrm{r}^{3}}{\mathrm{~s}}$

Accepted Answer

The correct simplification is $\left(\frac{\mathrm{r}}{\mathrm{s}}\right)^{3}=\frac{\mathrm{r}^{3}}{\mathrm{s}^{3}}$.

Question 4

Write the word or phrase that best completes each statement or answers the question.
-Simplify the expressions $(2 x)^{0}$ and $\left(2 x^{0}\right)$ and explain how you arrived at your answers.

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Write the word or phrase that best completes each statement or answers the question.
-When is the square of the sum the sum of a square; i.e., when is $(A+B)^{2}=A^{2}+B^{2}$ ?

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Write the word or phrase that best completes each statement or answers the question.
-What must be done to the dividend before beginning the "long division" process for $\left(5 a^{3}+8 a^{4}+2 a^{2}+6 a+5\right) \div(6 a+6) ?$

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Rank the numbers in order from smallest to largest.
$3.45 \times 10^{3}, 8.44 \times 10^{5}, 2.79 \times 10^{-5}, 3.48 \times 10^{3}, 5.02 \times 10^{-6}$
A) $8.44 \times 10^{5}<3.48 \times 10^{3}<3.45 \times 10^{3}<2.79 \times 10^{-5}<$
$5.02 \times 10^{-6}$
B) $5.02 \times 10^{-6}<3.45 \times 10^{3}<3.48 \times 10^{3}<8.44 \times 10^{5}<$
$2.79 \times 10^{-5}$
C) $2.79 \times 10^{-5}<5.02 \times 10^{-6}<3.45 \times 10^{3}<3.48 \times 10^{3}<$
$8.44 \times 10^{5}$
D) $5.02 \times 10^{-6}<2.79 \times 10^{-5}<3.45 \times 10^{3}<3.48 \times 10^{3}<$
$8.44 \times 10^{5}$

Accepted Answer

The correct order from smallest to largest is determined by the exponent of 10. Negative exponents indicate numbers less than 1, with smaller (more negative) exponents indicating smaller numbers. Positive exponents indicate numbers greater than 1, with larger exponents indicating larger numbers. Therefore, $5.02 \times 10^{-6}$ is the smallest, followed by $2.79 \times 10^{-5}$, $3.45 \times 10^{3}$, $3.48 \times 10^{3}$, and $8.44 \times 10^{5}$ is the largest.

Question 8

Tell whether or not the number is given in scientific notation. $1.543 \times 10^{-9}$

Accepted Answer

The number $1.543 \times 10^{-9}$ is in scientific notation because it is written as a product of a number between 1 and 10 and a power of 10.

Question 9

Tell whether or not the number is given in scientific notation. $59.34 \times 10^{-12}$

Accepted Answer

In scientific notation, the number before the multiplication sign should be between 1 and 10. Here, 59.34 is not between 1 and 10.

Quiz 10: Polynomials: Operations

Perform the division. - $\frac{-6 x^{3}-11 x^{2}+22 x-8}{3 x-2}$

Perform the division. - $\frac{-8 x^{3}+28 x^{2}-10 x-11}{2 x-5}$

Provide an appropriate response. - $\left(\frac{\mathrm{r}}{\mathrm{s}}\right)^{3}=\frac{\mathrm{r}^{3}}{\mathrm{~s}}$

Write the word or phrase that best completes each statement or answers the question. -Simplify the expressions $(2 x)^{0}$ and $\left(2 x^{0}\right)$ and explain how you arrived at your answers.

Write the word or phrase that best completes each statement or answers the question. -When is the square of the sum the sum of a square; i.e., when is $(A+B)^{2}=A^{2}+B^{2}$ ?

Write the word or phrase that best completes each statement or answers the question. -What must be done to the dividend before beginning the "long division" process for $\left(5 a^{3}+8 a^{4}+2 a^{2}+6 a+5\right) \div(6 a+6) ?$

Rank the numbers in order from smallest to largest. $3.45 \times 10^{3}, 8.44 \times 10^{5}, 2.79 \times 10^{-5}, 3.48 \times 10^{3}, 5.02 \times 10^{-6}$

Tell whether or not the number is given in scientific notation. $1.543 \times 10^{-9}$

Tell whether or not the number is given in scientific notation. $59.34 \times 10^{-12}$

Quiz 10: Polynomials: Operations

Perform the division. - −6x3−11x2+22x−83x−2\frac{-6 x^{3}-11 x^{2}+22 x-8}{3 x-2}3x−2−6x3−11x2+22x−8​

Perform the division. - −8x3+28x2−10x−112x−5\frac{-8 x^{3}+28 x^{2}-10 x-11}{2 x-5}2x−5−8x3+28x2−10x−11​

Provide an appropriate response. - (rs)3=r3 s\left(\frac{\mathrm{r}}{\mathrm{s}}\right)^{3}=\frac{\mathrm{r}^{3}}{\mathrm{~s}}(sr​)3= sr3​

Write the word or phrase that best completes each statement or answers the question. -Simplify the expressions (2x)0(2 x)^{0}(2x)0 and (2x0)\left(2 x^{0}\right)(2x0) and explain how you arrived at your answers.

Write the word or phrase that best completes each statement or answers the question. -When is the square of the sum the sum of a square; i.e., when is (A+B)2=A2+B2(A+B)^{2}=A^{2}+B^{2}(A+B)2=A2+B2 ?

Write the word or phrase that best completes each statement or answers the question. -What must be done to the dividend before beginning the "long division" process for (5a3+8a4+2a2+6a+5)÷(6a+6)?\left(5 a^{3}+8 a^{4}+2 a^{2}+6 a+5\right) \div(6 a+6) ?(5a3+8a4+2a2+6a+5)÷(6a+6)?

Rank the numbers in order from smallest to largest. 3.45×103,8.44×105,2.79×10−5,3.48×103,5.02×10−63.45 \times 10^{3}, 8.44 \times 10^{5}, 2.79 \times 10^{-5}, 3.48 \times 10^{3}, 5.02 \times 10^{-6}3.45×103,8.44×105,2.79×10−5,3.48×103,5.02×10−6

Tell whether or not the number is given in scientific notation. 1.543×10−91.543 \times 10^{-9}1.543×10−9

Tell whether or not the number is given in scientific notation. 59.34×10−1259.34 \times 10^{-12}59.34×10−12

Perform the division. - $\frac{-6 x^{3}-11 x^{2}+22 x-8}{3 x-2}$

Perform the division. - $\frac{-8 x^{3}+28 x^{2}-10 x-11}{2 x-5}$

Provide an appropriate response. - $\left(\frac{\mathrm{r}}{\mathrm{s}}\right)^{3}=\frac{\mathrm{r}^{3}}{\mathrm{~s}}$

Write the word or phrase that best completes each statement or answers the question. -Simplify the expressions $(2 x)^{0}$ and $\left(2 x^{0}\right)$ and explain how you arrived at your answers.

Write the word or phrase that best completes each statement or answers the question. -When is the square of the sum the sum of a square; i.e., when is $(A+B)^{2}=A^{2}+B^{2}$ ?

Write the word or phrase that best completes each statement or answers the question. -What must be done to the dividend before beginning the "long division" process for $\left(5 a^{3}+8 a^{4}+2 a^{2}+6 a+5\right) \div(6 a+6) ?$

Rank the numbers in order from smallest to largest. $3.45 \times 10^{3}, 8.44 \times 10^{5}, 2.79 \times 10^{-5}, 3.48 \times 10^{3}, 5.02 \times 10^{-6}$

Tell whether or not the number is given in scientific notation. $1.543 \times 10^{-9}$

Tell whether or not the number is given in scientific notation. $59.34 \times 10^{-12}$