Polynomials:

Simple curves are polynomials of various degrees, or orders. The degree is the integer of the highest exponent in the expression. The illustrations are as follows:

• A straight line is the first order or degree 1 polynomial of the form ax + b, or more clearly ax¹+ b.
• A quadratic is a second order (or degree 2) polynomial of the form ax² + bx + c.
• A cubic (degree 3) is of the form ax³ + bx² + cx + d.

A MATLAB represents a polynomial as a row vector of coefficients. For illustration, the polynomial x³ + 2x² - 4x + 3 would be represented by the vector [1 2 -4 3].

The polynomial 2x⁴ - x² + 5 would be represented by [2 0 -1 0 5]; note that the zero terms for x³ and x¹.

There are built-in functions sym2poly and poly2sym which convert symbolic expressions to polynomial vectors and vice versa, the illustration is as shown below:

>> myp = [1,2,-4,3];

>> poly2sym(myp)

ans =

x^3+2*x^2-4*x+3

>> mypoly = [2 0 -1 0 5];

>> poly2sym(mypoly)

ans =

2*x^4-x^2+5

>> sym2poly(ans)

ans =

2 0 -1 0 5