ALGEBRAIC EXPRESSIONS.

32. Degree of a Term.

A term that is the product of three letters is said to be of the third degree; a term of four letters is of the fourth degree; and so on.

Thus, $5abc$ is of the third degree; $2a^2{b}^2{c}^2$, that is, $2aabbcc$, is of the sixth degree.

33. Degree of a Compound Expression.

The degree of a compound expression is the degree of that term of the expression which is of the highest degree.

Thus, $a^2{x}^2+bx+c$ is of the fourth degree, since $a^2{x}^2$ is of the fourth degree.

34. Dominant Letter.

It often happens that there is one letter in an expression of more importance than the rest, and this is, therefore, called the dominant letter. In such cases the degree of the expression is generally called by the degree of the dominant letter.

Thus, $a^2{x}^2+bx+c$ is of the second degree in $x$.

35. Arrangement of a Compound Expression.

A compound expression is said to be arranged according to the powers of some letter when the exponents of that letter, reckoning from left to right, either descend or ascend in the order of magnitude.

Thus, $3a{x}^3-4b{x}^2-6ax+8b$ is arranged according to the descending powers of $x$, and $8b-6ax-4b{x}^2+3a{x}^3$ is arranged according to the ascending powers of $x$.