Polynomials and Rational Theorem Algebra Questions

Related BrainMass Solutions

• Polynomials

  5108 Solving 5 Example Algebra Problems Use the Rational Zero Theorem to list possible rational zeros for the polynomial: P(x) =x^3+3 x^2-6x-8 Use Descartes' Rule of Signs to determine both the number of possible positive and the number of possible

• Polynomials over the Rational Field: Monic Polynomial: If a is rational and x - a divides an integer monic polynomial, prove that a must be an integer.

  123121 Polynomials over the Rational Field: Monic Polynomial: If a is rational and x - a divides an integer monic polynomial, prove that a must be an integer.

• Ring Theory: Greatest Common Divisor (GCD)

  111047 Ring Theory: Greatest Common Divisor (GCD) Please respond to the following question: Find the greatest common divisor of the following polynomials over F, the field of rational numbers: x^3 - 6x^2 + x + 4 and x^5 - 6x + 1 Please see the attached

• Irreducible Polynomials

  For any d >= 1, ((x)^q)^d - x is the product of all monic irreducible polynomials in F_q[x] whose degree divides 'd'. ( See Theorem 14.2 Modern Computer Algebra, Joachim von zur Gathen, et.al.

• Polynomials over the Rational Field: Euclidean Ring: Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.

  Modern Algebra Ring Theory (XXXIII) Polynomials over the Rational Field Euclidean Ring

• Using Rational Zero Theorem for finding Roots of a Polynomial

  655082 Using Rational Zero Theorem for finding Roots of a Polynomial Use the Rational Zero Theorem to find all zeros of the following polynomials.

• Assorted Algebra - Inequalities, Remainders, Signs etc.

  543958 Assorted Algebra - Inequalities, Remainders, Signs etc. Please find my algebra questions in the file attached. They are mostly on inequalities, remainder theorem and Descartes' rule of signs among other topics. 1.

• Solving Inequality and Finding Zeros of Polynomials

  The solution gives detailed steps on solving the given inequalities and finding the zeros of given polynomials. Also, a step of factoring the polynomial is shown and explained if some factors are given.

• Elementary Algebra: Basic Operations with Polynomials

  263499 Elementary Algebra: Basic Operations with Polynomials Elementary Algebra: Basic Operations with Polynomials) 2. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ? A.