Question 1

Which of the following is the correct result when dividing $$3x^3$$ - $$7x^2 + 11x - 2$ by x - 3$ using long division?

Accepted Answer

$$3x^2 + 2x + 17$$ + \frac{49}{x-3}$$

Question 2

Given the polynomial $$f(x) = 3x^3$ + 4x^2$ - 5x + 3$$, what is the remainder when $$f(x) is $$divided by $$x + 2$$?

Accepted Answer

$$-13$$

Question 3

Which of the following statements best describes the Remainder Theorem?

Accepted Answer

The remainder when a polynomial $$f(x) is $$divided by $$x - c is$$ $$f(c).$$

Question 4

If $$x + 1 is a $$factor of $$f(x) = x^3$ - 7x^2$ + 6x$$, what is the value of $$f(-1)$$?

Accepted Answer

$$0$$

Question 5

Which of the following is NOT a correct step in the process of long division of polynomials?

Accepted Answer

Arrange the terms of both the dividend and the divisor in ascending powers of the variable.

Question 6

Use synthetic division to divide $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$. What is the remainder?

Accepted Answer

$$1$$

Question 7

A chemist is modeling the concentration of a substance with the polynomial $$C(x) = 4x^3$ - 2x^2$ + 7x - 9. $$According to the Remainder Theorem, what is the concentration when $$x = 2$$?

Accepted Answer

$$23$$

Question 8

Given $$f(x) = x^3$ + 2x^2$ - 5x + 6$$, which of the following is a factor of $$f(x)$$?

Accepted Answer

$$x - 2$$

Question 9

If the remainder when dividing $$f(x) by$$ $$x - 4 is$$ $$0$$, what can be concluded about $$f(x)$$?

Accepted Answer

$$x - 4 is a $$factor of $$f(x).$$

Question 10

A company models its profit with $$P(x) = 2x^3$ - 5x^2$ + 3x - 8. $$Using the Remainder Theorem, what is the profit when $$x = -1$$?

Accepted Answer

$$-12$$

Question 11

Which of the following is the correct quotient and remainder when dividing $$x^3$$ - $$2x^2 + 4x - 8$ by x - 2$?

Accepted Answer

$$x^2 + 0x + 4$ with remainder 0$

Question 12

If $$f(x) = 2x^3$ - 3x^2$ + 4x - 5$$ and $$f(1) = -2$$, what is the remainder when $$f(x) is $$divided by $$x - 1$$?

Accepted Answer

$$-2$$

Question 13

A medical researcher uses the polynomial $$M(x) = x^3$ - 6x^2$ + 11x - 6 to $$model the spread of a disease. If $$x = 1 is a $$zero of $$M(x)$$, what does this imply?

Accepted Answer

$$x - 1 is a $$factor of $$M(x).$$

Question 14

Which of the following is the correct setup for synthetic division when dividing $$4x^3$$ - $$2x^2 + 7x - 9$ by x + 3$?

Accepted Answer

Use $$c = -3$$ and coefficients $$4, -2, 7, -9$$

Question 15

If a polynomial $$f(x) is $$divided by $$x - c$$ and the remainder is $$r$$, which equation is always true?

Accepted Answer

$$f(c) = r$$

Question 16

A student divides $$x^3$$ + $$2x^2 - 5x + 6$ by x - 2$ and gets a remainder of 0$. What does this mean?

Accepted Answer

$$x - 2 is a $$factor of $$x^3$$ + $$2x^2 - 5x + 6$

Question 17

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

Accepted Answer

If $$f(a) = 0$$, then $$x - a is a $$factor of $$f(x).$$

Question 18

A real-world scenario: The height $$h (in $$meters) of a projectile is modeled by $$h(t) = -5t^2$ + 20t + 15. $$Using the Remainder Theorem, what is the height at $$t = 2$$ seconds?

Accepted Answer

$$35$$

Question 19

Which of the following is the correct result of dividing $$2x^3$$ + $$3x^2 - x + 4$ by x - 1$ using synthetic division?

Accepted Answer

$$2x^2 + 5x + 4$ with remainder 8$

Dividing Polynomials; Remainder and Factor Theorems

Study Guide - Practice Questions

Study Guide - Flashcards