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# 3rd Grading Reviewer/Quick notes on Math VII Essay

* Algebra – is a branch of mathematics that focuses on demonstrating the properties and relationships of abstract things in symbolic form or in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set. * Variable – is a symbol, usually a letter, such as x, y, or z, used to represent an unknown number. * Constant – an object or symbol that does not change its value in a particular problem or discussion e.g. pi. * Algebraic Expression – is a collection of numbers, variables, symbols for operations, and symbols for grouping.

* Diophantus – a Greek mathematician in the 3rd century, was for some time called the “Father of Algebra”. * Musa al-Khowarizimi – an Arabian mathematician in the 9th century was awarded the title the “Father of Algebra”. The word algebra was taken from his treatise Al-jabr. * Polynomial – is an algebraic expression that represents a sum of one or more terms containing whole-number exponents on the variables. In a polynomial, a variable cannot appear (1) in a denominator, (2) as an exponent, or (3) within a radical sign.

* A term is that part of an algebraic expression separated by + or – signs. Ex: 7x + 3 has two terms: 7x and 3. (7x is a variable term while 3 is a constant term). * The numerical part of a term is called its numerical coefficient. Ex: the numerical coefficient of 9m is 9, the numerical coefficient of –15x3y2 is –15, the numerical coefficient of x is 1. * Terms with exactly the same variables that have the same exponents are called like or similar terms. * Dissimilar terms are terms whose literal factors are not exactly alike. Ex. 3xy^2; 3x^2y; * Monomial – a polynomial with one term * Binomial – a polynomial with two terms * Trinomial – a polynomial with three terms

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