Exam (elaborations)
Nelson
- Institution
- 12th Grade
Exam of 10 pages for the course at 12th Grade (Great resource)
[Show more]
Seller
Follow
Content preview
MHF4U1-ASSIGNMENT CHAPTER 2 A NAME:___________________________True/False
Indicate whether the statement is true or false.
____ 1. When performing long division of a polynomial by a linear binomial, the degree of the remainder is always
smaller than the degree of the divisor.
____ 2. If P(–3) = 0 for a polynomial P(x), then x + 3 is a factor of P(x).
____ 3. For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.
____ 4. All quartic polynomial equations have at least one real solution.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 5. If x3 – 4x2 + 5x – 6 is divided by x – 1, then the restriction on x is
a. x –4 c. x 1
b. x –1 d. no restrictions
____ 6. What is the remainder when x4 + 2x2 – 3x + 7 is divided by x + 2?
a. 25 c. 37
b. 13 d. 9
____ 7. If 6x4 – 2x3 – 21x2 + 7x + 8 is divided by 3x – 1 to give a quotient of 2x3 – 7x and
a remainder of 8, then which of the following is true?
a.
b. 6x4 – 2x3 – 21x2 + 7x + 8 = (3x – 1)(2x3 – 7x) + 8
c.
d. all of the above
____ 8. When P(x) = 4x3 – 4x + 1 is divided by 2x – 3, the remainder is
a. c.
b. P(3) = 97 d.
____ 9. For a polynomial P(x), if P = 0, then which of the following must be a factor of P(x)?
a. c. 5x + 3
b. 3x + 5 d. 5x – 3
____ 10. Which of the following binomials is a factor of x3 – 6x2 + 11x – 6?
a. x – 1 c. x + 7
b. x + 1 d. 2x + 3
____ 11. Which set of values for x should be tested to determine the possible zeros of x3 – 2x2 + 3x – 12?
, a. 1, 2, 3, 4, 6, and 12 c. ±1, ±2, ±3, ±4, and ±6
b. ±1, ±2, ±3, ±4, ±6, and ±12 d. ±2, ±3, ±4, ±6, and ±12
____ 12. Determine the value of k so that x – 3 is a factor of x3 – 3x2 + x + k.
a. k = 3 c. k = 1
b. k = –3 d. k = –1
____ 13. Find k if 2x + 1 is a factor of kx3 + 7x2 + kx – 3.
a. k = –2 c.
k=
b. k = 2 d. none of the above
____ 14. Which of the following is the fully factored form of x3 + 3x2 – x – 3?
a. (x + 3)(x2 – 1) c. x2(x + 3) – (x + 3)
b. (x – 1)(x + 1)(x + 3) d. (x2 – 1)(x – 3)
____ 15. Which of the following is the fully factored form of x3 – 6x2 – 6x – 7?
a. (x – 7)(x + 1)2 c. (x – 7)(x2 + x + 1)
b. (x – 7)(x + 1)(x – 1) d. (x – 6)(x + 1)(x – 1)
____ 16. Which of the following is the factored form of x4 – 2x2 – 3?
a. (x – 1)(x + 1)(x – 3) c. (x2 + 1)(x2 – 3)
b. (x – 1)(x + 3)
2
d. none of the above
____ 17. One root of the equation x3 + 2x – 3x2 – 6 = 0 is
a. –3 c. 3
b. –1 d. 1
____ 18. What is the maximum number of real distinct roots that a quartic equation can have?
a. infinitely many c. 2
b. 4 d. none of the above
____ 19. If 2 is one root of the equation 4x3 + kx – 24 = 0, then the value of k is
a. –1 c. 8
b. –4 d. impossible to determine
____ 20. Based on the graph of f(x) = x4 – 2x3 + 3x + 2 shown, what are the real roots of x4 – 2x3 + 3x + 2 = 0?
a. 2 c. impossible to determine
b. –2, –1, 1, 2 d. no real roots
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller smith12345811. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$14.54. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
60281 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now