Red

Red is the color at the end of the spectrum of visible light next to orange and opposite violet. Red color has a predominant light wavelength of roughly 620–740 nanometres. Red is one of the additive primary colors of visible light, along with green and blue, which in Red Green Blue (RGB) color systems are combined to create all the colors on a computer monitor or television screen. Red is also one of the subtractive primary colors, along with yellow and blue, of the RYB color space and traditional color wheel used by painters and artists.

Reds can vary in shade from very light pink to very dark maroon or burgundy; and in hue from the bright orange-red scarlet or vermilion to the bluish-red crimson.

Red was widely used in prehistoric cave art, made with red hematite or iron oxide, or red ochre. Early civilizations in China, the Middle East and Europe made red dyes from the madder plant or from a tiny insect called Kermes vermilio. Civilizations in the Americas made brilliant reds from another scale insect, the cochineal; ancient Chinese artists during the Han Dynasty used dye from the madder plant to color silk and pigments from lead oxide to color pottery.

Crossbreed

A crossbreed or crossbred usually refers to an organism with purebred parents of two different breeds, varieties, or populations. Crossbreeding, sometimes called "designer crossbreeding", refers to the process of breeding such an organism, often with the intention to create offspring that share the traits of both parent lineages, or producing an organism with hybrid vigor. While crossbreeding is used to maintain health and viability of organisms, irresponsible crossbreeding can also produce organisms of inferior quality or dilute a purebred gene pool to the point of extinction of a given breed of organism.

The term is also used at times to refer to a domestic animal of unknown ancestry where the breed status of only one parent or grandparent is known, though the term "mixed breed" is technically more accurate. The term outcross is used to describe a type of crossbreeding used within a purebred breed to increase the genetic diversity within the breed, particularly when there is a need to avoid inbreeding.

Synthetic division

In algebra, synthetic division is a method of performing polynomial long division, with less writing and fewer calculations. It is mostly taught for division by binomials of the form

but the method generalizes to division by any monic polynomial, and to any polynomial.

The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper than long division. Also, the subtractions in long division are converted to additions by switching the signs at the very beginning, preventing sign errors.

Synthetic division for linear denominators is also called division through Ruffini's rule.

Regular synthetic division

The first example is synthetic division with only a monic linear denominator .

Write the coefficients of the polynomial that is to be divided at the top (the zero is for the unseen 0x).

Negate the coefficients of the divisor.

Write in every coefficient of the divisor but the first one on the left.