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25 April, 2008

Polynomials -Points to remember

Important points to remember:
  • A polynomial of degree 1 is a linear polynomial. e.g. 2x+3, 3x-2 etc
  • A polynomial of degree 2 is a quadratic polynomial. e.g. 3x^2-3x+2 etc
  • A monomial has 1 term. e.g.4 , 5x , 3x^2 etc
  • A binomial has 2 terms. e.g. 2x+3 , 4x^-2 etc
  • Degree of a polynomial is exponent of the highest degree term. e.g. degree of 3x+3 is 1.
  • A real number k is called a zero of a polynomial P(x) if P(k) = 0.
  • Graph of a linear polynomial is a straight line.
    Graph of a quadratic polynomial is a parabola.
  • A polynomial of degree n has atmost n zeroes.
  • Geometrically the zeroes of a polynomial are x coordinates of points where the graph of polynomial cuts/touches the x-axis.
  • Relationship between zeroes and coefficients of a quadratic polynomial : In a quadratic polynomial ax^2+bx+c, a not equal to zero, a,b,c, are real numbers

Sum of zeroes = - coefficient of x/coefficient of x^2

Product of zeroes = constant term/coefficient of x^2

  • Division Algorithm

Dividend = Divisor X Quotient + Remainder

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