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Number Theory

Classifying polynomials as monomials, binomials and trinomials

After completing please Classify the 15 given polynomials as monomials, binomials, trinomials, and polynomials. Use the format given below for categorizing the polynomials. Remember to simplify BEFORE you classify! - a. 2x3+3x2 + 2x - 1 b. ax4 - bx2 c. 3a4 - 6a3 + 3a2 d. -4xyz e. 3ab - 7cd + 5ac f.

Factoring Expressions and Solving Equations

Please see the attached file for the fully formatted problems. 1. Factor completely. 25x2 + 80x + 64 A) Prime B) (5x + 8)2 C) (5x + 8)(5x - 8) D) (5x - 8)2 2. Factor completely. 15z2 + 14z - 8 A) (15z + 4)(z - 2) B) (3z - 4)(5z + 2) C) Prime D) (3z + 4)(5z - 2) 3. Write the expression in lowest t

C++ - polynomials implementation

Design and implement a class for dealing with polynomials. The polynomial a(n)x^n + a(n-1)x^(n-1) + . . . + a0 will be implemented as a linked list. Each node will contain and int value for the power of x and an int value for the corresponding coefficient. The polynomial operations should include addition, multiplication, an

Rational function and polynomials

The reason why polynomials are so important is that there is a theorem from Analysis that says that any continuous function defined on an interval of the real line can be approximated arbitrarily closely by a polynomial. So polynomials are useful to ¿model¿ any kind of function on a closed interval. However, polynomials ¿ge

Polynomials and rational function

Now consider a rational function, which is the ratio of two polynomials. These two polynomials will each have a set of zeros, and note that at a zero of the denominator we are actually dividing by zero. The zeros of the denominator are called poles, and they are point where the rational function becomes infinite (unless there

Exponents and Polynomials

Simplify. All variables represent nonzero real numbers. 1.) -5y^4 (y^5)^2 15y^7 (y^2)^3 2.) 3y^8 This whole problem is ^4 2zy^2 3.) 3^3 This whole problem is ^4

Time Sequence diagrams

Please reference this figure for the question: 55. Draw 3 time sequence diagrams that illustrate the flow of frames between points B and G in Figure 1 using the following information: a. Stop and Wait ARQ, SENDER sends four frames (F1, F2, F3, and F4). F1, F2 and F4 are received error free, but F3 is lost in the

Mersenne Primes

Determine whether m_13 = 2^13 - 1 = 8191 and m_23 = 2^23 -1 = 8388607 are prime.


See attachment, thank you very much. Simplify each expression 1. 2x3 . 3x2 (x3 = X raised to the power 3, x2 = X raised to the power 2). 2. (2x2 y)4 3. 18x4 divided by 3x or 18x4 ----------- 3x 4. x-9 = 5. 9x

Basic math

Please assist with attached math problems. 1 Write this number in expanded form a. 247,089 b. What digit tells the number of thousands c. What digit tell the number of ten thousands 2 Write this number in words $8,886 3 Name the property of addition and explain your choice. a. 3+(0 + 6) = (3 + 0) + 6 b. 0 + a

Marriage penalty eliminated ...

Marriage penalty eliminated. The value of the expression 4220 + 0.25(x - 30,650)is the 2006 federal income tax for a single taxpayer with taxable income of x dollars, where x is over $30,650 but not over $74,200. a) Simplify the expression. b) Find the amount of tax for a single taxpayer with taxable income of $40,000. c) W


I am attaching the problem Add the radicals... Multiply

Exercise on Polynomials

Solve the following questions involving fundamental operations on polynomials a. Find p(x) + 4q(x) p(x)=4x^4 + 55x^3 - 23x^2 + 13 q(x)=43x^4+ 14x^2 -12 b. Find P(-1/2) if P(x) = 2x^4 + x^3 + 12 c. Simplify: (-4 + x^2 + 2x^3) - (-6 - x + 3x^3) - (-6y^3 + y^2) d. Add: (2x^2 + 6y^2 + 4z^2 + 3xy + yz + zx) + (4x^2 + 3y^

Pigeonhole Principle - 1a. If X and Y are infinite sets with the same number of elements, show that the following conditions are ... 1b. Suppose there are 11 pigeons sitting in some pigeonhole ...

1a. If X and Y are infinite sets with the same number of elements, show that the following conditions are equivelent for a function f: X-->Y: (i). f is injective (ii). f is bijective (iii) f is surjective 1b. Suppose there are 11 pigeons sitting in some pigeonhole. If there are only 10 pigeonholes prove that there is a h

Performing Division Calculations

Perform the following division: (9x^3 - 19x + 8)/(-3x +4). Write your answer in the form Q(x) + (R(x))/(-3x + 4), where Q(x) is the quotient and R(x) is the remainder of the division.

Contemporary Abstract Algebra, Author: Joseph A. Gallian

Chapter 0 (Preliminaries) Q.) How would you prove the converse? A partition of a set S defines on equivalence relation on S. Hint: Define a relation as X - Y if X and Y are elements of the same subset of the partition. 10.) Let n be fixed positive integer greater than 1. If a mod n = a' and b mod n = b' .Prove that (a

Exponentials, Multiplication, Division of Polynomials

See attached. 1. Evaluate the expression. Assume 2. Evaluate when y = -2 3. Evaluate when 4. Express the following using a positive exponent. Then simplify the expression . Write using a positive exponent do not evaluate 5. Express using a positive exponent = 6. Multiply and simplify =

Integers, whole numbers, natural numbers, rational numbers, irrational numbers

Directions: List all numbers from the given set B that are members of the given Real Number subset. Please explain. B=[ 19, square root 8, -5, 0, 0.7 as a repeating decimal, square root of 9] Integers B= [ 17, square root of 5, -2, 0,0.7 as a repeating decimal, square root 16,] Whole numbers B= [ 6,square root v8,

Prime numbers, factors, division

1. List the first seven prime numbers of our standard number system (0, 1, 2, 4, 4, etc...) 2. List all the factors for the number 72 3. Which of the numbers 21, 88, 126 and 255 are divisible by 7.

Polynomials with Real and Complex Solutions

1. The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. 2. Find the inverse of the function f(x) = x1/3 + 2. 3. If a piece of real estate purchased for $50,000 in 1998 appr

Polynomials and Complex Roots

State how many complex and real zeros the functon has. x^2 -2x+7 x^4-2x^2+3x-4 find all of the zeros and write a linear factorization of the function f(x)=x^3+4x-5 r(x)=3x^4+8x^3+6x^2+3x-2 using the given zero, find all of the zeros and write a linear factorization of f(x) 1+i is a zero of f(x)=x^4-2x^3-x^2+