KENDRIYA VIDYALAYA
DHARANGDHRA,
MILATRY AREA
CLASS-9’A
NAME-CH.HARI-NARAYAN.
Polynomials
Each term of a polynomial is a product of a
constant (coefficient) and one or more variables
whose exponents a...
Polynomial
• The graph of a polynomial function of degree 3.In
mathematics, a polynomial is an expression of finite
length...
3.1 Review on Polynomials
(A) Monomials and Polynomials
A monomial is a an algebraic
expression containing one term, which...
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

− ...
The degree of a polynomial is equal to the
highest degree of its terms.

The terms of a polynomials are usually
written in...
Equality of Polynomials
If two polynomials in x are equal for
all values of x, then the two
polynomials are identical, and...
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...
(B) Remainder Theorem

9

3 28
27

28 = 3 x 9 + 1
dividend
divisor

remainder

quotient

1
Applications of Theorems about
Polynomials

(A)Use Factor Theorem to factorize a
polynomial of degree 3 or above

(1) try ...
4. X-y=(x +y) (x -y)

(1) (3x+2) (3x-2)
= (3x) –(2)
=9x -4
(7x-5) (7x+5)
=(7x) – (5)
=49x - 25
Maths Presentation Ppt
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

  1. 1. KENDRIYA VIDYALAYA DHARANGDHRA, MILATRY AREA CLASS-9’A NAME-CH.HARI-NARAYAN.
  2. 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. 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. 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. 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. 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. 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. 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. 9. (B) Remainder Theorem 9 3 28 27 28 = 3 x 9 + 1 dividend divisor remainder quotient 1
  10. 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. 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. 12. Maths Presentation Ppt

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