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In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form โ + + โ to the form โ + โ for some values of โ โ and โ โ . [1] In terms of a new quantity โ x − h {\displaystyle x-h} โ , this expression is a quadratic polynomial with no linear term.
The formula for the difference of two squares can be used for factoring polynomials that contain the square of a first quantity minus the square of a second quantity. For example, the polynomial can be factored as follows:
Notice also that the set obtained by forming all the combinations a + b √ 2, where a and b are integers, is an example of an object known in abstract algebra as a ring, and more specifically as an integral domain. The number ω is a unit in that integral domain. See also algebraic number field.
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
Word problem from the Lฤซlฤvatฤซ (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
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