Calculating the roots of a polynomial function.

Find the roots. X^3 + 4*x^2 +6x -2 =0

Understanding the formulas for compound interest.

What is the equation to compute loan payment for a multimonth car loan at a fixed interest?

Modern algebra

(a) Let G = GL(2,R) be the general linear group. Let H=GL(2,Q) and K= SL(2,R) = {A is an element of G: det (A) =1} Show that H,K are subgroups of G (b) Let p be a prime number and a is an element of Z. Prove that a^p ,is equivalent to, a mod p

Modern algebra

(a) Let F = { (matrix with first row; a 0, second row is 0 a) : a is an element of R Show that F is a field and that F ~= R (b) Give the definition of a cyclic group Prove that every subgroup H of a cyclic group G = is itself cyclic

Subgroups of cyclic groups

Show that any subgroup of a cyclic group is cyclic.

Simplifying complex polynomial expressions.

Simplify: (a/(a-b))+(b/a^2+ab+b^2))- (2/(a^3-b^3)

When is Z/nZ a field?

Show that Z/nZ is a field if and only if n is a prime.

Solving equalities.

Solve the open sentence. If there are no solutions or if it is true for all real numbers then indicate so. x + 11 < -1 or -1/2x < -4

Simplex Method

1. Maximize C = 5x1 + 4x2 + 3x3 Subject to the constraints x1 + x2 + x3 < = 100 2x1 + x2 + < = 50 x1 > = 0 x2 > = 0 x3 > =0

Finding the equations of lines in slope intercept form.

Find the equation of the line with slope 0 and which passes through the point (-2,-9)