Ad
related to: how to divide monomials with exponents step by step problemsThis site is a teacher's paradise! - The Bender Bunch
- Educational Songs
Explore catchy, kid-friendly tunes
to get your kids excited to learn.
- Lesson Plans
Engage your students with our
detailed lesson plans for K-8.
- Interactive Stories
Enchant young learners with
animated, educational stories.
- Education.com Blog
See what's new on Education.com,
explore classroom ideas, & more.
- Educational Songs
Search results
Results from the WOW.Com Content Network
Lexicographic order (lex) first compares exponents of x 1 in the monomials, and in case of equality compares exponents of x 2, and so forth. The name is derived from the similarity with the usual alphabetical order used in lexicography for dictionaries, if monomials are represented by the sequence of the exponents of the indeterminates.
In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
The degree of a monomial is defined as the sum of all the exponents of the variables, including the implicit exponents of 1 for the variables which appear without exponent; e.g., in the example of the previous section, the degree is + +. The degree of is 1+1+2=4. The degree of a nonzero constant is 0.
This pen-and-paper method uses the same algorithm as polynomial long division, but mental calculation is used to determine remainders. This requires less writing, and can therefore be a faster method once mastered. The division is at first written in a similar way as long multiplication with the dividend at the top, and the divisor below it.
A polynomial has a square root if and only if all exponents of the square-free decomposition are even. In this case, a square root is obtained by dividing these exponents by 2. Thus the problem of deciding if a polynomial has a square root, and of computing it if it exists, is a special case of square-free factorization.
In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials.The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate consequence of the definition of a polynomial).
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Ad
related to: how to divide monomials with exponents step by step problemsThis site is a teacher's paradise! - The Bender Bunch