Polynomials of degree three are called cubic polynomials . • Polynomial of degree four are called quartic polynomials . It is customary to write polynomials in descending powers of x . That is, we write polynomials having the term of highest power (leading term) as the first term and the constant term as the last term.
For instance, and x y are equations in three variables x , y , z ; x is an equation in one variable x . In the earlier classes we have solved trigonometric equations, system of linear equations, and some polynomial equations. - - We know that is a zero of the polynomial x and is a root or solution of the equation . We note that cos and cos = are also equations in one variable x .
However, cos and cos − are not polynomials and hence cos = are not “polynomial equations”. We are going to consider only “polynomial equations” and equations which can be solved using polynomial equations in one variable. We recall that sin = is an identity on , while sin = and sin are equations. It is important to note that the coefficients of a polynomial can be real or complex numbers, but the exponents must be nonnegative integers.
For instance, the expressions x − + and x + are not polynomials. We already learnt about polynomials and polynomial equations, particularly about quadratic equations. In this section let us quickly recall them and see some more concepts.