Mathematics Chapter 2 Polynomials | Class 9th | PPT
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This document contains notes from Vedant Patil's 9th grade summer homework. It defines key algebraic terms like constants, variables, algebraic expressions, polynomials. It classifies polynomials based on degree like linear, quadratic, cubic etc. and based on number of terms like monomial, binomial, trinomial. It also defines constant polynomials, zeros of a polynomial and algebraic identities.
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Mathematics Chapter 2 Polynomials | Class 9th | PPT
- 2. SUMMER VACATION HOME WORK SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th
- 3. • Definition of Constant • Definition of Variable • Definition of Algebraic expression. • Definition of Polynomial • Classification of polynomials on the basis of degree. • Classification of polynomials on the basis of number of terms. • Definition of Constant Polynomial. • Zero of a Polynomial • Algebric Identities SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th
- 4. Definition of Constant SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th A symbol having fixed numerical value is called a Constant Example : 8 ; 1/3 ; -62 ; 155 ; 23/98 etc. are Constant
- 5. Definition of Variable SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th A symbol which may be assigned different numerical values is known a Variable. Example : C = 2π r Circumference of Circle ( r – radius ; 2& π are constants ; where C & r are Variables)
- 6. Definition of Algebric Expression SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th A combination of constants and variables. Connected by some or all of the operations +, -, X and is known as algebraic expression. Example : 4y²+12z-3 ; 4/9x³y – 5/6a etc.
- 7. Definition of Polynomial SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th An algebraic expression in which the variables involved have only nonnegative integral powers is called a polynomial. Example : 8x² + 69x¾ - 9x² - 2x³ in variable x. 54y³+4y – 68y² + 2y in variable y.
- 8. Classification of Polynomial on Basis of Degree Degree Polynomial Example • 1 Linear y+1, 5x-2 etc. • 2 Quadratic ba²+x-ax etc. • 3 Cubic xy³- 6ab etc. • 4 Biquadratic a¼ + 2xa SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th
- 9. Classification of Polynomial on Basis of Number of Terms No. of Terms Polynomial Example • 1 Monomial 8 ; 5x ; 7/15 • 2 Binomial 6x+9y ; 4ab – 9x • 3 Trinomial 9a- 2xy²+12/29+xy SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th
- 10. Definition Of Constant Polynomial A polynomial containing one term only, consisting a constant term is called a constant polynomial the degree of non-zero constant polynomial is zero. SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th
- 11. SANSKAR PUBLIC SCHOOL : VEDANT PATIL 9th Definition of Algebric Identities The algebraic equations which are valid for all values of variables in them are called algebraic identities. There are 3 Algebric Identities : • (a + b)2 = a2 + 2ab + b2 • (a – b)2 = a2 – 2ab + b2 • a2 – b2= (a + b)(a – b)