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a₁ adding applying approach arranged assign b₁ called chance changed coefficients common factor complex constant contains continued convergent corresponding defined definition denominator denote derived determinant divide divisible equal equation exactly Example EXERCISE expression factor figure finite formula four fraction function given graph greater Hence identity increases indicate infinite integral involve irrational less letters limit mean method multiply namely negative Observe obtain pair particular polynomial positive possible powers preceding prime prove quotient radical rational reckoning reduced remainder respectively result roots rule sequence Show simple Simplify solution Solve square root Substituting subtract suppose theorem third tion transformed true unknown values vanishes variable write
Page 98 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 80 - ... 1. a + b = b + a. 2. a + (b + c) = (a. + b) + c. 3.
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.
Page 13 - EQUALITY 1. If a = b, then a + c = b + c. 2. If a = b, then a — c = b — c. 3. If a = b, then ac = be.