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Published on: **Mar 4, 2016**

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- 1. POLYNOMIAL Submitted by Kavitha.M Reg No:13971007 Mathematics Option
- 2. Polynomial A Polynomial is defined as a single terms or a sum of a finite number of terms. In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials appear in a wide variety of areas of mathematics and science
- 3. LIKE TERMS "Like terms" are terms whose variables are the same. In other words, terms that are "like" each other. Example: 7x x -2x Are all like terms because the variables are all x. Add like terms together to make one term: Example: 7x + x They are both like terms, so you can just add them: 7x + x = 8x
- 4. Polynomial Addition Sum of two polynomials, we need only add the coefficient of equal powers. The constant terms should also be added. Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in. Eg: Simplify (2x + 3) + (4x + 6) = 2x + 3 + 4x + 6 = 2x+4x+9 =6x+9
- 5. Polynomial Subtraction Difference of two polynomial, we need only subtract the coefficient of equal powers.To subtract two polynomials subtract like terms. Eg : Simplify (2x + 3) – (4x+6) = 2x+3-4x-6 = (2x-4x)+(3-6) = -2x-3 =-(2x+3)
- 6. POLYNOMIAL MULTIPLICATION To multiply polynomial ,multiply each term of the first polynomial by each term of the second polynomial and then combine like terms Example: (2x+5)(4x-3)=(2xx4x)+(2x x-3)+(5x4x)+(5x-3) =8x²+6x+20x+15 =8x²+26x+15
- 7. MULTIPLICATION AND ADDITION For any three numbers x,y,z , xz+yz=(x+y)z If there is a common polynomial among these then there is no need to multiply twice and add . Example: (2x+1)(3x+4)+(4x+3)(3x+4) here the polynomial (3x+4)is common for both =((2x+1)+(4x+3))(3x+4) =(6x+4)(3x+4) =18x²+24x+12x+16 =18x²+36x+16
- 8. Degree of polynomial The degree of polynomial is the largest exponent occuring in its terms. Eg : 8x²+ 3x + 4 Degree of polynomial = 2 A polynomial whose degree ‘ 1’ is called first degree polynomial, a polynomial whose degree ‘ 2’ is called second degree polynomial.
- 9. Conclusion Polynomials are one of the most important topics in mathematics. For this reason, it is important that you learn polynomials well. Moreover, polynomials are great ways to develop a particular thinking skill. Polynomials should be studied both because they are one of the most frequently discussed objects in mathematics and because they are one of the most interesting.