- a polynomial in one variable x

is represented by the array of all its coefficients

- in this representation, one needs for the polynomial

to store coefficients even though only nonzero coefficients are really necessary; for polynomials in more variables, the situation is even worse

- the time complexity of the algorithm for adding two polynomials
of degree in this representation is of the order
; polynomials can have high degree and only a
few terms so that most of the operations are unnecessary (such as
the addition of two zero coefficients)
- most polynomials which we encounter in real life are sparse, that
is, most of their coefficients are zero

Richard Liska