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` .