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Math 140 Exam 3 Sample - Polynomials and Functions, Exams of Algebra

Iowa State University (ISU)Algebra

A sample exam for math 140 exam 3, which covers topics related to polynomials and functions. The exam includes problems on determining the degree, leading coefficient, and leading term of a polynomial function, finding zeros and their multiplicity, quotients and remainders, function values, and factoring polynomial functions. It also includes problems on using the intermediate value theorem and finding the domain, x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptotes of a function.

Typology: Exams

Pre 2010

Uploaded on 09/02/2009

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koofers-user-g28 ๐Ÿ‡บ๐Ÿ‡ธ

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Sample Exam for Exam 3 Math 140 Section C
Instructions: This is a sample exam for Exam 3 which is on Mar. 27. 2009. All problems in Exam
3 will be similar to the problems in this sample exam. Please notice that the number of problems in
Exam 3 will be more than it is in this sample exam.
1. Determine the degree, the leading coefficient and the the leading term of the given polynomial
function.
(a) f(x)=2x3+6x2โˆ’x4+11 Degree:
Leading coefficient:
Leading term:
(b) g(x)=x(3xโˆ’5)(x+1)3Degree:
Leading coefficient:
Leading term:
2. Find the zeros of the given polynomial function and state the multiplicity of each.
(a) f(x)=(xโˆ’3)4(x2+16)2
(b) g(x)=(xโˆ’1)3(2x+4)
3. Find the quotient and the remainder of each following.
(a) (x4+3x3+2xโˆ’5) รท(xโˆ’1)
Quotient:
Remainder:
(b) (x5โˆ’3x2+6) รท(x+3)
Quotient:
Remainder:
1
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Download Math 140 Exam 3 Sample - Polynomials and Functions and more Exams Algebra in PDF only on Docsity!

Sample Exam for Exam 3 Math 140 Section C Instructions: This is a sample exam for Exam 3 which is on Mar. 27. 2009. All problems in Exam 3 will be similar to the problems in this sample exam. Please notice that the number of problems in Exam 3 will be more than it is in this sample exam.

  1. Determine the degree, the leading coefficient and the the leading term of the given polynomial function. (a) f (x) = 2 x^3 + 6 x^2 โˆ’ x^4 + (^11) Degree: Leading coefficient: Leading term: (b) g(x) = x(3x โˆ’ 5)(x + 1)^3 Degree: Leading coefficient: Leading term:
  2. Find the zeros of the given polynomial function and state the multiplicity of each. (a) f (x) = (x โˆ’ 3)^4 (x^2 + 16)^2

(b) g(x) = (x โˆ’ 1)^3 (2x + 4)

  1. Find the quotient and the remainder of each following. (a) (x^4 + 3 x^3 + 2 x โˆ’ 5) รท (x โˆ’ 1) Quotient: Remainder:

(b) (x^5 โˆ’ 3 x^2 + 6) รท (x + 3) Quotient: Remainder:

  1. Find the indicated function value for each given polynomial function. (a) f (x) = 2 x^3 โˆ’ 6 x^2 + x โˆ’ 4 and find f (โˆ’3).

(b) g(x) = โˆ’ 2 x^5 + x^3 + 11 x^2 โˆ’ 4 x + 12 and find g(2).

  1. Find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros. (a) โˆ’4, โˆ’ โˆš 3

(c) 3 + 2 i, 7 โˆ’ โˆš5, 8

  1. List all possible rational zeros. (a) x^4 โˆ’ 2 x^3 + 7 x + 4

(b) 5x^5 โˆ’ 11 x^4 + 2 x^3 โˆ’ 6 x^2 โˆ’ 6 x + 3

  1. Factor each of the following polynomial function into linear factors. (a) f (x) = x^3 + 4 x^2 + 4 x + 16

(b) g(x) = x^4 โˆ’ x^3 โˆ’ 19 x^2 + 49 x โˆ’ 30