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algebraic approach arithmetical progression arranged ascending powers binomial binomial theorem called coefficients coeﬁicients common factor complex numbers constant convergent convergent series corresponding cube root deﬁned deﬁnition denominator denote derived diﬁerent digits divide divisor equal exactly divisible exponents expression ﬁgure ﬁnal ﬁnd ﬁnding ﬁnite ﬁrst degree ﬁve following example formula given equation graph Hence highest common factor identity imaginary inﬁnite integers integral function irrational number last number leading term less limit logarithms lower degree method multiply natural numbers nth root obtain pair of equations partial fractions perfect square polynomial positive number prime factors proper fraction prove quadratic quotient radical radicand rational number real numbers reduced remainder respect result rules of reckoning sequence simple equations Simplify solution square root Substituting subtract suppose symmetric functions synthetic division tion transformed unknown letters values vanishes variable Wehave
Page 96 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 104 - To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sab — 12ac) -i- 4a = 36 — 3c.
Page 530 - For if we picture complex numbers by points in a plane in the manner described in § 238 and draw a circle whose center is at the origin and whose radius is...
Page 114 - Transpose the unknown terms to the first member, and the known terms to the second. Unite the similar terms, and divide both members by the coefficient of the unknown quantity.
Page 427 - In every algebraic equation, the coefficient of whose highest term is unity, the coefficient pi of the second term with its sign changed is equal to the sum of the roots. The coefficient...
Page 372 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 444 - Suppose now a polynomial formed of the product of the factors corresponding to the negative and imaginary roots of an equation ; the effect of multiplying this by each of the factors x - a, x...