Question 1

Divide the polynomial $$6x^2 - 15x + 8$ by the monomial 2x$. What is the result?

Accepted Answer

$$3x - \frac{15}{2} + \frac{4}{x}$$

Question 2

What is the result of dividing $$x^8 by$$ $$x^5$$?

Accepted Answer

$$x^3$$

Question 3

Divide $$10x^3$$ - $$5x^2 + 20x$ by 5x$. What is the simplified result?

Accepted Answer

$$2x^2 - x + 4$

Question 4

Which of the following is the correct application of the quotient rule for exponents: $$\frac{a^m}{a^n}$$?

Accepted Answer

$$a^{m-n}$$

Question 5

Divide $$8y - 16x^5$y^4$$ - $$5x^6y^2$ + 7xy by$$ $$4xy^2. $$What is the result?

Accepted Answer

$$2y^{-1}$$ - $$4x^4y^2$ - \frac{5}{4}x^5$ + \frac{7}{4}$

Question 6

What is the result of dividing $$3x^5y^2$ - 15x^3$y - x^2$y - 6x by$$ $$x^2y$?

Accepted Answer

$$3x^3y$$ - $$15x^2 - 1$$ - $$6x^{-1}y$$^{-1}$

Question 7

Using long division, what is the quotient when $$6x^2 - 19x + 12$ is divided by 3x - 5$?

Accepted Answer

$$2x - 3$$

Question 8

Divide $$(6x^2 + 11x - 2$$)$$ by (x + 2$$)$$ using long division. What is the quotient?

Accepted Answer

$$6x + 1$$

Question 9

What is the result of dividing $$27x^3 + 8$ by 3x + 2$ using long division?

Accepted Answer

$$9x^2 - 6x + 4$

Question 10

Using synthetic division, what is the quotient when $$2x^3$$ - $$x^2 - 13x + 1$ is divided by x - 3$?

Accepted Answer

$$2x^2 + 5x + 2$

Question 11

Which value should be used in synthetic division when dividing by $$x + 2$$?

Accepted Answer

$$-2$$

Question 12

Divide $$4x^3$$ - $$3x^2 + 6x + 5$ by x - 1$ using synthetic division. What is the quotient?

Accepted Answer

$$4x^2 + x + 7$

Question 13

Divide $$x^4$$ - $$2x^3$$ - $$11x^2 + 34$ by x + 2$ using synthetic division. What is the quotient?

Accepted Answer

$$x^3$$ - $$4x^2 - 3x + 6$

Question 14

Divide $$y^3 - 8$ by y - 2$ using synthetic division. What is the quotient?

Accepted Answer

$$y^2 + 2y + 4$

Question 15

A chemist is preparing a solution and needs to divide $$20x^3$$ - $$8x^2 + 5x + 5$ by 5x - 2$. What is the quotient?

Accepted Answer

$$4x^2 - x + 1$

Question 16

A medical researcher is analyzing a polynomial model for drug concentration: $$2x^3$$ - $$6x^2 - 4$. If the time variable is divided by (x - 4$$)$$, what is the quotient?

Accepted Answer

$$2x^2 + 2x + 8$

Question 17

Divide $$(10x^3$$ - $$5x^2 - 12x + 1$$)$$ by (2x - 1$$)$$ using long division. What is the quotient?

Accepted Answer

$$5x^2 - x - 7$

Question 18

A historian is modeling population growth with the polynomial $$5x^3$$ + $$9x^2 - 10x + 2$. If the model is divided by (x + 3$$)$$, what is the quotient?

Accepted Answer

$$5x^2 - 6x + 8$

Question 19

Divide $$4x^7y^4$ + 8xy^2$ + 4xy^3$ by 4xy^3$. What is the result?

Accepted Answer

$$x^6y$$ + $$2y^{-1} + 1$

Dividing Polynomials: Long Division and Synthetic Division

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