High School Math Contest University of South Carolina February 5, 2011 Solutions
... 29. (b) All together there are 27 ways to color the vertices garnet or black – we shall refer to them as “patterns”. Let us count how many patterns correspond to the same coloring. Assume first that the coloring is non-trivial (not all vertices black or all garnet). In this case, a rotation of a pat ...
... 29. (b) All together there are 27 ways to color the vertices garnet or black – we shall refer to them as “patterns”. Let us count how many patterns correspond to the same coloring. Assume first that the coloring is non-trivial (not all vertices black or all garnet). In this case, a rotation of a pat ...
Student Handout Book.. - hrsbstaff.ednet.ns.ca
... 2) Determine if it is a repeating or terminating decimal (rational) or not (irrational). Example 1: Classifying Numbers Tell whether each number is rational or irrational. Explain how you know! a) ...
... 2) Determine if it is a repeating or terminating decimal (rational) or not (irrational). Example 1: Classifying Numbers Tell whether each number is rational or irrational. Explain how you know! a) ...
Ex - Alliance Gertz-Ressler High School
... order that the words were written in and copied that for the algebraic expression. They ignored the fact that we need 17 less than the unknown amount, meaning we start with an unknown amount and then take 17 away from it. ...
... order that the words were written in and copied that for the algebraic expression. They ignored the fact that we need 17 less than the unknown amount, meaning we start with an unknown amount and then take 17 away from it. ...
Factorization
In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms.Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.