In mathematics, a polynomial (from Greek poly, "many" and medieval
Latin binomium, "binomial" is an expression of finite length constructed from variables (also known as indeterminates)
and constants, using only the
operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x^{2} − 4x + 7 is a polynomial, but x^{2} − 4/x + 7x^{3/2} is not, because its second term involves division by the
variable x (4/x) and because its third
term contains an exponent that is not a whole number (3/2).
http://en.wikipedia.org/wiki/Polynomial
Sum/difference of two squares
A
visual illustration of the identity (a + b)^{
2} = a^{2} + 2ab + b^{2}^{ }(Our
solved example in mathguru.com uses this concept)
Another common type of algebraic factoring is called the difference of two squares. It is the application of the formula
to any two terms, whether or not they are perfect squares. If the
two terms are subtracted, simply apply the formula. If they are added, the two
binomials obtained from the factoring will each have an imaginary term. This
formula can be represented as
For example, 4x^{2} + 49 can be factored into (2x + 7i) (2x − 7i).
Factoring other polynomials
Sum/difference of two cubes
Another formula for factoring is the sum or difference of two
cubes. The sum can be represented by
and the difference by
For example, x^{3} − 10^{3} (or x^{3} − 1000) can be factored into (x − 10) (x^{2} + 10x + 100). (Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Factorization
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