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Constant, , A number having a fixed numerical value is called a constant., , 2, Examples: 2,3, 7,8, 14 5, ete,, , Variable, , A number which can take various numerical values is known as a variable., , Examples: x, y, z, etc., , A number which is a power of another variable where the power is not zero is also a variable., Examples: x3, y?, 24, etc., , A number which is the product of a constant and a variable is also a variable., , Examples: 5x, 8x3, 8x, etc., , ‘A combination of two or more variables separated by a ‘+’ sign or a ‘sign is also a variable., , , , Examples: x2— y+ 28,23 + y+ 2, ete., , Algebraic Expression, , , , A combination of constants and variables connected by, an algebraic expression., , Examples: 8x2 + 5, 4x3 + 2xy — 8xy? + 6, etc., , or ~ or ‘’ or ‘+’ signs is known as, , Terms, , Several parts of an algebraic expression, separated by ‘+’ or ‘~’ signs are called the terms of the, expression., , Example: In the expression, 8x — 14y + 9, we say that 8x, — 14y and 9 are terms., , Coefficient of a Term, , Consider the term 9x4. In this case, 9 is called the numerical coefficient of x* and x‘ is said to be, the literal coefficient of 9., , In case of 6xy, the numerical coefficient is 6 and the literal coefficient is xy., , 145, , Like Terms, The terms having the same literal coefficients are called like terms., , Examples: (i) 2x, -6x+ and 9x4 are like terms., (ii) 18x2y8, -1522y3 and 17x2y3 are like terms., , Unlike Terms, The terms having different literal coefficients are called unlike terms., , Example: 13x, 17x, 14x are unlike terms., , Polynomial, , An algebraic expression in which the variables involved have only non-negative integer powers, is called a polynomial., , Example: 3y + 4x2—7, 2x3 + 4y? — 8x + 9, etc., , The expression 5x4 — 7x3 + 9x? — 3x5”? is not a polynomial since it has powers of x which are, negative and fractions., , A polynomial that contains only one variable is known as a polynomial in that variable., , Example: 8x + 15 is a polynomial in the variable x and 2y? + 2y3 is a polynomial in the, variable y., , A polynomial that contains two variables, say x and y is known as a polynomial in two variables., , Example: x3? — 2x4y3 + 5xy is a polynomial in x and y variables., , Degree of a Polynomial in One Variable, , The highest exponent of the variable in a polynomial of one variable is called the degree of the, polynomial., , Examples: (a) x4 —5x2—x + 7 is a polynomial of degree 4., (b) 7x? — 3x6 + 723 — x? — 5 is a polynomial of degree 9.