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3.1. Degree

A general univariate (having one variable) polynomial is written as:

anxn + an-1xn-1 + an-2xn-2 + . . . + a2x2 + a1x + a0
A general bivariate (having two variables) polynomial is written as:
anmxnym + . . . a22x2y2 + a21x2y + a12xy2 + a11xy + a10x + a01y + a00
The degree of a polynomial is the degree of the term with the highest sum of integer powers of the variables. The general univariate polynomial shown above has degree n; the general bivariate polynomial has degree n + m. The following are examples of polynomials
exampletypedegree
12xmonomial1
3.2x + 1.4ybinomial1
x3y2z2 + 2x2 + 3xy2z3 trinomial7
Univariate polynomial expressions have these special names:
expressionnamedegree
aconstant0
ax + blinear1
ax2 + bx + cquadratic2
ax3 + bx2 + cx + dcubic3
ax4 + bx3 + cx2 + dx + equartic4
ax5 + bx4 + cx3 + dx2 + ex + f quintic5


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Copyright © 2005, Stephen R. Schmitt