Question 1

Which of the following best describes the first step when dividing $$2x^3$$ - $$5x^2 - 8x + 15$ by x - 3$ using long division?

Accepted Answer

Divide $$2x^3 by$$ $$x to $$get $$2x^2$$

Question 2

What is the result of dividing $$y^2 - 5y + 6$ by y - 2$?

Accepted Answer

$$y - 3$$ with a remainder of $$0$$

Question 3

Using synthetic division, what is the remainder when $$2x^3$$ - $$5x^2 - 8x + 15$ is divided by x - 3$?

Accepted Answer

$$0$$

Question 4

If $$P(x) = 4x^6$ - 25x^3$ + 35x^4$ + 17x^2$, what is P(4$$)$$ using the Remainder Theorem?

Accepted Answer

$$P(4) = 4099$$

Question 5

Divide $$12x^5$$ + $$4x^4$$ - $$12x^2 - 4x$ by 3x + 1$. What is the leading term of the quotient?

Accepted Answer

$$4x^4$$

Question 6

If a polynomial is divided by $$x - 6$$, the quotient is $$2x^2 + 4x - 3$ and the remainder is 7$. What is the original polynomial?

Accepted Answer

$$(x - 6)(2x^2$ + 4x - 3) + 7$$

Question 7

Which of the following is a correct application of the Remainder Theorem?

Accepted Answer

The remainder when $$P(x) is $$divided by $$x - a is$$ $$P(a)$$

Question 8

A chemist is mixing two solutions. The concentration of the first solution is modeled by $$C(x) = 3x^2$ - 2x + 5. If $$the chemist wants to know the concentration when $$x = 2$$, what theorem can be used to find the answer quickly?

Accepted Answer

The Remainder Theorem

Question 9

Which of the following is NOT a valid step in synthetic division?

Accepted Answer

Subtract the divisor from each coefficient

Question 10

A company models its profit with $$P(x) = 2x^3$ - 5x^2$ + 4x - 8. If $$the company wants to know the profit when $$x = 2$$, what is the value?

Accepted Answer

$$0$$

Question 11

Which of the following best describes the relationship between the degree of the dividend and the degree of the divisor in polynomial long division?

Accepted Answer

The degree of the quotient is the difference between the degrees of the dividend and divisor

Question 12

If $$P(x) is $$divided by $$x - 2$$ and the remainder is $$5$$, what is $$P(2)$$?

Accepted Answer

$$5$$

Question 13

A medical researcher models the spread of a virus with $$V(x) = x^3$ - 6x^2$ + 11x - 6. $$What is the remainder when $$V(x) is $$divided by $$x - 1$$?

Accepted Answer

$$0$$

Question 14

Which of the following is the correct quotient when dividing $$x^2 - 4$ by x - 2$?

Accepted Answer

$$x + 2$$

Question 15

A student divides $$x^3$$ + $$2x^2 - x - 2$ by x + 1$ using synthetic division. What is the remainder?

Accepted Answer

$$0$$

Question 16

Which of the following is a real-world application of dividing polynomials?

Accepted Answer

Calculating the average speed of a car over time when speed is modeled by a polynomial

Dividing Polynomials: Long Division, Synthetic Division, and Remainder Theorem

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