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Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
Hari narayan class 9-a
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Hari narayan class 9-a

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  • 1. KENDRIYA VIDYALAYA DHARANGDHRA, MILATRY AREA CLASS-9’A NAME-CH.HARI-NARAYAN.
  • 2. Polynomials Each term of a polynomial is a product of a constant (coefficient) and one or more variables whose exponents are non-negative integers. e.g. –6a3, 4x3 + x, 3y4 + 2y2 + 1, 6x2y2 – xy + y -ve e.g. 4 4a , 5 x , x +1 −2
  • 3. Polynomial • The graph of a polynomial function of degree 3.In mathematics, a polynomial is an expression of finite length constructed from variables (also called indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. However, the division by a constant is allowed, because the multiplicative inverse of a non zero constant is also a constant. For example, x2 − x/4 + 7 is a polynomial, but by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2). The term "polynomial" can also be used as an adjective, for quantities that can be expressed as a polynomial of some parameter, as in polynomial time, which is used in computational complexity theory
  • 4. 3.1 Review on Polynomials (A) Monomials and Polynomials A monomial is a an algebraic expression containing one term, which may be a constant, a positive integral power of a variable or a product of powers of variables. e.g. 4, 2x3 and 3x2y
  • 5. quotient − x − 2x + 1 4 3 2 − x + 0 x + 4 x − 3x + 1 divisor dividend − x + 2x − x 4 3 2 2 − 2 x + 5 x − 3x 3 2 − 2x + 4x − 2x 3 2 x −x + 1 2 x 2 −2 x + 1 remainder x
  • 6. The degree of a polynomial is equal to the highest degree of its terms. The terms of a polynomials are usually written in descending order (i.e. the terms are arranged in descending degree).
  • 7. Equality of Polynomials If two polynomials in x are equal for all values of x, then the two polynomials are identical, and the coefficients of like powers of x in the two polynomials must be equal.
  • 8. Alternative Method When x = 2, 3(2)2 - 5(2) - 5 = [A+3(2)](2-2) + B 12-10-5 = B B = -3 When x = 0, 3(0)2 - 5(0) – 5 = [A+3(0)](0-2) + B -5 = -2A + B -5 = -2A – 3 -2 = -2A A=1
  • 9. (B) Remainder Theorem 9 3 28 27 28 = 3 x 9 + 1 dividend divisor remainder quotient 1
  • 10. Applications of Theorems about Polynomials (A)Use Factor Theorem to factorize a polynomial of degree 3 or above (1) try to put a = +1, -1, +2, -2, +3, -3, …. one by one into the polynomial until the function is equal to zero. (2) as the function is equal to zero, then (x – a) is one of the factors. (3) divide the polynomial by (x – a) to get the quotient which is the other factor of the polynomial. (4) factorize the quotient by the method you have learnt in before.
  • 11. 4. X-y=(x +y) (x -y) (1) (3x+2) (3x-2) = (3x) –(2) =9x -4 (7x-5) (7x+5) =(7x) – (5) =49x - 25
  • 12. Maths Presentation Ppt

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