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 $$12x^5y^2$ + 14x^2$y^7 by$$ $$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 $$x^6y^3$ - 9x^4$y^2$$ + $$14x^2y$ divided by 7x^2$y. $$What is the simplified expression?

Accepted Answer

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

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Simplify the following expression:

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

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 $$\frac{6a^2$b^2$$ - $$12ab^2$$}{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 $$14x^4y^3$ - 49x^3$y^2$$ + $$7x^2y$ by 7x^2$y. $$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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