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Example:Solving Quadratic by Factorization

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In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is

where x represents a variable, and a, b, and c, constants, with a ≠ 0. (If a = 0, the equation becomes a linear equation.)

The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square". Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula




In mathematics, factorization (also factorisation in 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.  The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an "expanded" polynomial, written as just a sum of terms.

A visual illustration of the polynomial

x2 + c x + d = (x + a)(x + b) where a plus b equals c and a times b equals d.

(Our solved example in mathguru.com uses this concept).




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.