What are Polynomials
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This document provides an overview of polynomials. It defines polynomials as expressions with multiple terms where the exponents are whole numbers. Monomials have one term, binomials have two terms, and trinomials have three terms. Polynomials can have variables, constants, and exponents of whole numbers. Expressions with non-whole number exponents or fractions are not polynomials. The document also notes that polynomials of one variable can be written as a sum of terms with coefficients and descending exponents, and the highest exponent indicates the degree of the polynomial.
What are Polynomials
- 2. What are Polynomials • Polynomials means Poly( many) and nomials(terms). So it is many terms • It can have any term having constants ,variable and exponents but the exponents should be whole number • So all these are polynomial x+1 , 5 , 5-x, 11x –y3 , x+y+z 1+2y+2y2 ,1 .2 x +y , 6x-2
- 3. Polynomial continued • These are not polynomial √𝑥 2/x+2 x-2 Why? As the exponent is not whole number • Polynomials are also classified based on number terms One term Monomial Two term Binomial Three terms trinomial
- 4. Polynomial on One variable 𝑆 𝑥 = 𝑎 𝑛 𝑥 𝑛 + 𝑎 𝑛−1 𝑥 𝑛−1 + 𝑎 𝑛−2 𝑥 𝑛−2 + ⋯ … … … + 𝑎𝑥 + 𝑎0 Points to remember an, an-1…………. Coefficient of xn, xn-1 n Called the degree of polynomial If S(x)=0 It is called zero polynomial If S(x) =a0 It is called constant polynomial If for x=a S(x)=0 a is the called zero of polynomial
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