College AlgebraScott, Foresman, 1901 - 777 páginas |
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Página xviii
... FORMULA FOR THE EXPANSION OF A BINOMIAL 591 592 593 595 598 599 600 601 606 Product of n Different Binomial Factors 610 Characteristics of the Binomial Expansion 612 Maximum Coefficient of Binomial Expansion 615 Summation of the Same ...
... FORMULA FOR THE EXPANSION OF A BINOMIAL 591 592 593 595 598 599 600 601 606 Product of n Different Binomial Factors 610 Characteristics of the Binomial Expansion 612 Maximum Coefficient of Binomial Expansion 615 Summation of the Same ...
Página 58
... Formula IX translated , is : The product of the quotient by the divisor is equal to the dividend . The number of times a group of 4 individuals can be counted out of another group of 4 things is 1 , or a group of a things out of another ...
... Formula IX translated , is : The product of the quotient by the divisor is equal to the dividend . The number of times a group of 4 individuals can be counted out of another group of 4 things is 1 , or a group of a things out of another ...
Página 65
... formula : D = qd + R. That is , the dividend is equal to product of the quotient , at any stage , by the divisor , plus the remainder at this stage . Thus , and . ' . 4959 + 1 = 91 ; .. 499 × 5 + 4 x2 + x - 9 ÷ ( x + 3 ) = x − 2 — 3 x ...
... formula : D = qd + R. That is , the dividend is equal to product of the quotient , at any stage , by the divisor , plus the remainder at this stage . Thus , and . ' . 4959 + 1 = 91 ; .. 499 × 5 + 4 x2 + x - 9 ÷ ( x + 3 ) = x − 2 — 3 x ...
Página 81
... formula , VI . ( ab ) ( a2 + ab + b2 ) = a3 — b3 . EXAMPLE . ( 3x - 2y ) ( 9 x2 + 6xy + 4y2 ) = ( 3x ) 3 Similarly by multiplication , ( 2 y ) 3 = 27x3 - 8 y3 . VII . ( a + b ) ( a2 — ab + b2 ) = a3 + b3 . EXAMPLE . ( 2x + y ) ( 4x2 ...
... formula , VI . ( ab ) ( a2 + ab + b2 ) = a3 — b3 . EXAMPLE . ( 3x - 2y ) ( 9 x2 + 6xy + 4y2 ) = ( 3x ) 3 Similarly by multiplication , ( 2 y ) 3 = 27x3 - 8 y3 . VII . ( a + b ) ( a2 — ab + b2 ) = a3 + b3 . EXAMPLE . ( 2x + y ) ( 4x2 ...
Página 93
... formula ) that ( 1 ) x2 + P1x2¬1 + + P - x + P1 = Q ( x − r ) + R - a relation which holds , whatever x may be ; hence , in equation ( 1 ) give the value r . Then + Pn - 1 " + P2 - ( 2 % 100 ] 93 FACTORING AND SOLUTION OF EQUATIONS.
... formula ) that ( 1 ) x2 + P1x2¬1 + + P - x + P1 = Q ( x − r ) + R - a relation which holds , whatever x may be ; hence , in equation ( 1 ) give the value r . Then + Pn - 1 " + P2 - ( 2 % 100 ] 93 FACTORING AND SOLUTION OF EQUATIONS.
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Términos y frases comunes
A₁ algebraic Arithmetic ax² b₁ binomial Binomial Theorem c₁ CHAPTER coefficients common convergent corresponding cube root decimal definition denominator determinant difference divided division divisor equal equivalent example exponent expression factors figures Find the number formula fraction given equation greater Hence imaginary increases inequality integer irrational less limit log 1+r logarithm mantissa mathematical induction monomial multiplied negative number nth root number of terms P₁ partial fractions polynomial positive integer positive number problem quadratic quadratic equation quotient rational remainder result rule satisfy second degree second member solution Solve the equations square root substituting subtraction Suppose surd symbols system of equations theorem third tion triangle trinomial unknown numbers unknown quantities Va² zero
Pasajes populares
Página 205 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 666 - Q(x) to obtain a quotient (polynomial of the form -Q ) plus a rational function (remainder divided by the divisor) in which the degree of the numerator is less than the degree of the denominator.
Página 79 - Raise the absolute value of the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Página 71 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Página 588 - What will $ 100 amount to in 7 years with interest at 8% per annum, compounded semi-annually ? 3. In how many years will a sum of money double itself at 6%, compounded annually ? 4.
Página 181 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.
Página 519 - In any proportion, the terms are in proportion by Alternation; that is, the first term is to the third as the second term is to the fourth.
Página 520 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 524 - The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples...
Página 588 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.