...dividend and divisor contain but two letters and are homogeneous, the degree of the quotient will be the excess of the degree of the dividend over that of the divisor. EXAMPLES. 1. Divide a4 — Ba'x — 8aV+18aa;'-fl62;4 by a' — 2ax — 2ж*. OPERATION. 1— 3—...

...dividend and divisor contain but two letters and are homogeneous, the degree of the quotient will be the excess of the degree of the dividend over that of the divisor. EXAMPLES. 1. Divide a4— 3a'x— 8aV+18ax'+16x* by a*— 2ax— 2x«. OPERATION. 1_3_8+18+16[1—...

...3° That the quotient of two homogeneous functions is a homogeneous function whose degree is equal to the excess of the degree of the dividend over that of the divisor; 4° That the power of a homogeneous function is a homogeneous function whose degree is equal to the...

...and divisor. Hence — When the quotient of two integral functions of x is an integral function of x, its degree is the excess of the degree of the dividend over the degree of the divisor. Thus, for example, the degree of (a;2- l)/(x- 1) is 2-1 = 1. 2. It may be...

...the given quotient. The integral part of the transformed function is called the Integral Quotient ; its degree is the excess of the degree of the dividend over the degree of the divisor, The numerator of the fractional part of the transformed function is called...

...divisor. The degree of the integral quotient obtained by the above Division Transformation is equal to the excess of the degree of the dividend over that of the divisor. The degree of the remainder which is used as the numerator of the fractional part of the transformed...