long division

(noun)

A procedure for division that involves breaking down a polynomial division into a series of easier steps.

Related Terms

Examples of long division in the following topics:

  • Dividing Polynomials

    • Polynomial long division is a method for dividing a polynomial by another polynomial of the same or lower degree.
    • For example, find the quotient and the remainder of the division of $x^3 - 12x^2 -42$, the dividend, by $x-3$, the divisor.
    • Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.This method is a generalized version of the familiar arithmetic technique called long division.It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
    • For example, find the quotient and the remainder of the division of $x^3 - 12x^2 -42$, the dividend, by $x-3$, the divisor.

  • Division and Factors

    • Polynomial long division functions similarly to long division, and if the division leaves no remainder, then the divisor is called a factor.
    • We want to find integers $q$ and $r$ such that $0 \leq r < d$ and $D = qd+r.$ This we can do with long division, which we all learned to do in elementary school.
    • The beauty of long division is that the algorithm can be used not for integers only, but also for polynomials.

  • The Remainder Theorem and Synthetic Division

    • In algebra, the polynomial remainder theorem or little Bézout's theorem, is an application of polynomial long division.
    • A shorthand way to perform long division is synthetic division.
    • It also takes significantly less space than long division.
    • Most importantly, the subtractions in long division are converted to additions by switching the signs at the very beginning, preventing sign errors.
    • This way we can still use synthetic division.

  • Meter

    • In other words, it is a question of division: does each beat divide into two equal parts, or three equal parts.
    • In compound meters, the bottom number of the time signature corresponds to the type of note corresponding to a single division of the beat.
    • If a compound meter is notated such that each dotted-quarter note corresponds to a beat, the eighth note is the division of the beat, and thus the bottom number of the time signature is 8.
    • If a compound meter is notated such that each dotted-half note corresponds to a beat, the quarter note is the division of the beat, and thus the bottom number of the time signature is 4.
    • Note that because the beat is divided into three in a compound meter, the beat is always three times as long as the division note, and the beat is always dotted.

  • Regulation of the Cell Cycle by External Events

    • External factors can influence the cell cycle by inhibiting or initiating cell division.
    • When a daughter cell divides, it turns into two new cells, which would lead to the assumption that each cell is capable of being immortal as long as its descendants can continue to divide.
    • However, all cells in the body only live as long as the organism lives.
    • A lack of HGH can inhibit cell division, resulting in dwarfism, whereas too much HGH can result in gigantism .
    • Crowding of cells can also inhibit cell division.

  • Transfer Pricing

    • They also tell the final assembly division in Indiana that they must make a profit of 2,000.
    • Each division must set a transfer price in which the company will be the most profitable and not based on each division being the most profitable.
    • For example, goods from the production division may be sold to the marketing division, or goods from a parent company may be sold to a foreign subsidiary, with the choice of the transfer price affecting the division of the total profit among the parts of the company.
    • Division managers are provided incentives to maximize their own division's profits.
    • That is to say, a firm should expand its output as long as the marginal revenue from additional sales is greater than their marginal costs.

  • Divisions of the Skeletal System: Axial and Appendicular

    • The skeletal system is divided into two distinct divisions: the axial skeleton and the appendicular system.
    • These are long bones, short bones, flat bones, irregular bones, and sesamoid bones.
    • It is a complex structure with two distinct divisions: the axial and the appendicular skeletons.

  • Dots, Ties, and Borrowed Divisions

    • So a dotted half note, for example, would last as long as a half note plus a quarter note, or three quarters of a whole note.
    • A dotted half lasts as long as a half note plus a quarter note.
    • If there might be any question as to which notes are involved in the borrowed division, a bracket is placed above them.
    • Triplets are by far the most common borrowed division.
    • Jazz or blues with a "swing" rhythm often assumes that all divisions are triplets.

  • Schein's Common Elements of an Organization

    • The four common elements of an organization include common purpose, coordinated effort, division of labor, and hierarchy of authority.
    • Managers communicate this purpose by educating all employees on the general strategy, mission statement, values, and short- and long-term objectives of the organization.
    • Division of labor is also known as work specification for greater efficiency.
    • Using division of labor, an organization can parcel out a complex work effort for specialists to perform.

  • Imperialism and Racial Divisions