Understanding the words group and pattern will help us understand Algebraic and Geometric patterns.

May 29th, 2015
Studypool Tutor
Price: $10 USD

Tutor description

A group is a number of things that we can see and touch that are related. They can be related based on any number of reasons. For example, the items may be in a group because they are the same color or size.

Word Count: 2631
Showing Page: 1/9
Principles of Classical AlgebraIn elementary algebra letters are used to stand for numbers. For example, in the equation ax2+bx+c=0, the letters a, b, and c stand for various known constant numbers called coefficients and the letter x is an unknown variable number whose value depends on the values of a, b, and c and may be determined by solving the equation. Much of classical algebra is concerned with finding solutions to equations or systems of equations, i.e., finding the roots, or values of the unknowns, that upon substitution into the original equation will make it a numerical identity. For example, x=-2 is a root of x2-2x-8=0 because (-2)2-2(-2)-8=4+4-8=0; substitution will verify that x=4 is also a root of this equation.The equations of elementary algebra usually involve polynomial functions of one or more variables (see function). The equation in the preceding example involves a polynomial of second degree in the single variable x (see quadratic). One method of finding the zeros of the polynomial function f(x), i.e., the roots of the equation f(x)=0, is to factor the polynomial, if possible. The polynomial x2-2x-8 has factors (x+2) and (x-4), since (x+2)(x-4)=x2-2x-8, so that setting either of these factors equal to zero will make the polynomial zero. In general, if (x-r) is a factor of a polynomial f(x), then r is a zero of the polynomial and a root of the equation f(x)=0. To determine if (x-r) is a factor, divide it into f(x); according to the Factor Theorem, if

Review from student

Studypool Student
" Thanks, good work "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1821 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors