# Polynomial of One Variable

The polynomial ax+b , where a,b are numbers (A!=0) and x is variable, is called first degree polynomial; the polynomial ax^2+bx+c , where a, b, c are numbers (a!=0) and x is variable, is called second degree polynomial (or trinomial square); the polynomial ax^3+bx^2+cx+d, where a, b, c, d are numbers (a!=0) and x is variable, is called third degree polynomial.

In general, if a, b, c,...,l,m are numbers (a!=0) and x is variable, then polynomial ax^n+bx^(n-1)+cx^(n-2)+...+lx+m is called polynomial of n-th degree (relative to x); ax^n, bx^(n-1),...,lx,m are members of polynomial; a, b, c,...,l,m are coefficients; ax^n is member with the highest degree; m is absolute term of polynomial. The polynomial we usually write in decreasing order of degrees of variable, i.e. the degrees of variable x gradually decreases (in particular, on the first place is senior member and on the last-absolute term) and this record is called the standart form of polynomial. The degree of polynomial is member with the highest degree.

For example, 5x^5-2x^3+3x^2+1 is the quintic polynomial, in which 5x^5 is member with the highest degree, 1 is absolute term of polynomial.

The root of polynomial P(x) is such value x for which value of polynomial equals zero.

For example, the number 2 is root of polynomial P(x)=x^3+2x^2-7x-2, because P(2)=2^3+2*2^2-7*2=0 .