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algebraic approach arithmetical progression arranged binomial binomial theorem called coefficients common factor complex numbers convergent convergent series corresponding cube root definition denominator denote descending powers digits divide divisor equal exactly divisible exponent expression factor x Find the H.C.F. following example formula given equation graph Hence highest common factor identity imaginary infinite integers integral function irrational number leading term less limit logarithms lower degree method monomial 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 roots of f(x rules of reckoning sequence simple equations Simplify solution square root Substituting subtract symmetric functions synthetic division tions transformed unknown letters vanishes variable
Page 98 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 499 - If all the elements of a, row (or column) are multiplied by the same number, as k, the determinant is multiplied by k.
Page 433 - Or we may enunciate the laws thus : the coefficient of the second term with its sign changed is equal to the sum of the roots ; the coefficient of the third term is equal to the sum of the products of...
Page 434 - Find the sum of the squares of the roots of the equation 2xa-3x2-4x- 5 = 0.
Page 378 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 450 - 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...
Page 109 - To divide a polynomial by a monomial, divide each term of the dividend by the divisor and add the partial quotients.
Page 233 - It must not be inferred, from what has just been said, that the conqueror can have no control or government of hostile territory, unless he occupies it with an armed force.