POLYNOMIALS

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  • Oxford dictionary definition: An expression of more than two algebraic terms , especially the sum of several terms that contain different powers of the same variable(s ).
  • Cambridge dictionary definition: A number or variable ( = mathematical symbol ), or the result of adding or subtracting two or more numbers or variables.
  • A polynomial is an algebraic expression in which the variables have non-negative integers exponent only and involves the operations of addition, subtraction, multiplication.
  • Examples are x^2 + 3x + 4,  4x^2 - 6x^2y^2 + x^3 + 7y^3 etc. 
  • The zeroes of polynomial are precisely the x-coordinates of the points, where the graph of y = p(x) intersect the x-axis.
  • The linear polynomial ax + b, a is not equal to zero, has exactly one zero.
  • Quadratic polynomial can have either two distinct or two equal zeroes or no zero. This implies the polynomial of degree 2 has atmost 2 zeroes.
  • Polynomial of degree 3 ( cubic polynomial ) can have atmost three zeroes.
  • If α and β are the zeroes of the quadratic polynomial ax^2 + bx + c, then α +  β = -b/a and αβ = c/a.
  • If α, β and γ are the zeroes of the cubic polynomial ax^3 + bx^2 + cx + d, then α +  β + γ = -b/a, αβ + βγ +  γα = c/a and αβγ = -d/a

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