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Chapter 1 Real Numbers

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  Chapter 1                                                                                        Real Numbers  Natural Numbers Non-negative counting numbers excluding zero are known as natural numbers. i.e. 5, 6, 7, 8,  ………. Whole numbers All non-negative counting numbers including zero are known as whole numbers. i.e. 0, 1, 2, 3, 4, 5, ……………. Integers All negative and non-negative numbers including zero altogether known as integers.  i.e. ………. – 3, – 2, – 1, 0, 1, 2, 3, 4, ………….. The Fundamental Theorem of Arithmetic We can factorize each composite number as a product of some prime numbers and of course, this prime factorization of a natural number is unique as the order of the prime factors doesn’t matter. HCF of given numbers is the highest commo...
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Chapter 2 Polynomials

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  Chapter 2 Polynomials A polynomial is an expression consists of constants, variables and exponents. It’s mathematical form is- a­­­ n x n  + a n-1 x n-1  + a n-2 x n-2  + a 2 x 2  + a 1 x + a 0  = 0 where the (a i )’s are constant Degree of Polynomials Let P(y) is a polynomial in y, then the highest #ffffcc power of y in the P(y) will be the degree of polynomial P(y). Types of Polynomial according to their Degrees Type of polynomial Degree Form Constant 0 P(x) = a Linear 1 P(x) = ax + b Quadratic 2 P(x) = ax 2  + ax + b Cubic 3 P(x) = ax 3  + ax 2  + ax + b Bi-quadratic 4 P(x) = ax 4  + ax 3  + ax 2  + ax + b Value of Polynomial Let p(y) is a polynomial in y and α could be any real number, then the value calculated after putting the value y = α in p(y) is the final value of p(y) at y = α. This shows that p(y) at y = α is represented by p (α). Zero of a Polynomial If the value of p(y) at y = k is 0, that is p (k) = 0 then y = ...
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