Question 1

Simplify the following expression and choose the correct answer:

$\frac{8n^2 - 36n}{4n}$

Accepted Answer

$2n - 9$

Question 2

A chemist is preparing a solution and needs to divide $12x^5y^2 + 14x^2y^7$ by $2x^2y^7$. What is the simplified result?

Accepted Answer

$6x^3y^{-5} + 7$

Question 3

Which of the following correctly applies the quotient rule for exponents to $\frac{a^8}{a^3}$?

Accepted Answer

$a^{5}$

Question 4

Divide and simplify: $\frac{18c^3 - 21c^2}{3c}$

Accepted Answer

$6c^2 - 7c$

Question 5

A biologist is analyzing the growth of bacteria modeled by $x^6y^3 - 9x^4y^2 + 14x^2y$ divided by $7x^2y$. What is the simplified expression?

Accepted Answer

$\frac{1}{7}x^4y^2 - \frac{9}{7}x^2y + 2$

Question 6

Simplify the following expression:

$\frac{40x^2 - 8x}{8x}$

Accepted Answer

$5x - 1$

Question 7

Which of the following is the correct simplification of $\frac{12k^2 - 20k}{4k}$?

Accepted Answer

$3k - 5$

Question 8

A physics student divides $18y^3 - 2y^2$ by $y$. What is the simplified result?

Accepted Answer

$18y^2 - 2y$

Question 9

Simplify the following expression:

$\frac{24w^4 + 14w^3 - 4w^2}{2w^2}$

Accepted Answer

$12w^2 + 7w - 2$

Question 10

A medical researcher divides $6a^2b^2 - 12ab^2$ by $2ab$. What is the simplified result?

Accepted Answer

$3ab - 6b$

Question 11

Which of the following is the correct simplification of $\frac{15x^5 + 25x^3 - 5x^2}{5x^2}$?

Accepted Answer

$3x^3 + 5x - 1$

Question 12

Simplify the following expression:

$\frac{28x^5y^4z^3 + 8x^4y^3z^2 + 4x^2y^2z}{4x^2y^2z}$

Accepted Answer

$7x^3y^2z^2 + 2x^2y + 1$

Question 13

A company’s profit is modeled by $45p^5q^3 - 60p^4q^2 + 15p^3q$ divided by $15p^3q$. What is the simplified expression?

Accepted Answer

$3p^2q^2 - 4pq + 1$

Question 14

Simplify the following expression:

$\frac{9m^3n^4 - 27m^2n^3 + 9mn^2}{9mn^2}$

Accepted Answer

$m^2n^2 - 3mn + 1$

Question 15

A student divides $18y^3 - 2y^2$ by $y$. What is the simplified result?

Accepted Answer

$18y^2 - 2y$

Question 16

Which of the following is the correct simplification of $\frac{6a^2b^2 - 12ab^2}{2ab}$?

Accepted Answer

$3ab - 6b$

Question 17

A real-world scenario: A rectangular garden has an area given by $24x^4 + 14x^3 - 4x^2$ square meters. If the width is $2x^2$ meters, what is the length in simplest form?

Accepted Answer

$12x^2 + 7x - 2$

Question 18

Simplify the following expression:

$\frac{27n^4 + 9n^3 - 63n^2}{9n^2}$

Accepted Answer

$3n^2 + n - 7$

Question 19

A scientist divides $14x^4y^3 - 49x^3y^2 + 7x^2y$ by $7x^2y$. What is the simplified result?

Accepted Answer

$2x^2y^2 - 7xy + 1$

Dividing Polynomials by a Monomial – Step-by-Step College Algebra Guidance

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