What are Polynomials What are Polynomials A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable. A one-variable (univariate) polynomial of degree n has the following form: anxn + an-1xn-1 + ... + a2x2 + a1x1 + ax where the a's represent the coefficients and x represents the variable. Because x1 = x and x = 1 for all complex numbers x, the above expression can be simplified to: anxn + an-1xn-1 + ... + a2x2 + a1x + a When an nth-degree univariate polynomial is equal to zero, the result is a univariate polynomial equation of degree n: anxn + an-1xn-1 + ... + a2x2 + a1x + a = 0 There may be several different values of x, called roots, that satisfy a univariate polynomial
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equation. In general, the higher the order of the equation (that is, the larger the value of n), the more roots there are. A univariate polynomial equation of degree 1 (n = 1) constitutes a linear equation. When n = 2, it is a quadratic equation; when n = 3, it is a cubic equation; when n = 4, it is a quartic equation; when n = 5, it is a quintic equation. The larger the value of n, the more difficult it is to find all the roots of a univariate polynomial equation. Some polynomials have two, three, or more variables. A two-variable polynomial is called bivariate; a three-variable polynomial is called trivariate. a polynomial is an expression constructed from variables(also known as indeterminates) and constants,using various operations A polynomial is a finite length expression constructed from variables (also known as indeterminates) and constants, by using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents. For example, x2 − 4x + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term involves division by the variable x and also because its third term contains an exponent that is not a whole number.
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One more example of find the size of the angle if two angles are complementary with each other as Example no (4) : If the size of one angle that is angle 1 is 60 ' and size of other angle that is angle 2 is not given and these given angles angle 1 and angle 2 are complementary with each other then find the size of angle 2 ? Solution : As give that the angle 1 and angle 2 are complementary angles and these are denoted as angle 1 – angle 2 = 90 ' angle 1 = 60 ' and angle 2 = ? Then angle 2 = 90 ' - angle 1 angle 2 = 90 ' - 60 ' angle 2 = 30 '
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