A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 sider |
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Side viii
... Remainder Theorem . An expression of the nth degree cannot vanish for more than n values of x , unless it vanishes for all values of a Cyclical order Symmetrical expressions . Factors found by use of Remainder Theorem Examples VI . · 53 ...
... Remainder Theorem . An expression of the nth degree cannot vanish for more than n values of x , unless it vanishes for all values of a Cyclical order Symmetrical expressions . Factors found by use of Remainder Theorem Examples VI . · 53 ...
Side 47
... remainder must be the product of the divisor by the sum of all the other terms of the quotient ; and , this remainder being also arranged according to descending powers of a , the second term of the quotient will be found as before by ...
... remainder must be the product of the divisor by the sum of all the other terms of the quotient ; and , this remainder being also arranged according to descending powers of a , the second term of the quotient will be found as before by ...
Side 48
By Charles Smith Charles Smith. 2ab2 + b3 , and there is no remainder . Since there is no remainder after the last subtraction , the dividend must be equal to the sum of the different quantities which have been subtracted from it ; but ...
By Charles Smith Charles Smith. 2ab2 + b3 , and there is no remainder . Since there is no remainder after the last subtraction , the dividend must be equal to the sum of the different quantities which have been subtracted from it ; but ...
Side 50
... remainder . Hence by proceeding far enough we must come to a stage where there is no remainder , or else where there is a remainder such that the highest power of a in it is less than the highest power of a in the divisor , and in this ...
... remainder . Hence by proceeding far enough we must come to a stage where there is no remainder , or else where there is a remainder such that the highest power of a in it is less than the highest power of a in the divisor , and in this ...
Side 66
... remainder is 2a ” , so that x " + a ” is never divisible by x - a . If we change a into a becomes x − ( − a ) = x + a ; also x " - a " becomes x " - ( -a ) ” , and x " − ( − a ) ” is x2 + a ” a " according as n is odd or even ...
... remainder is 2a ” , so that x " + a ” is never divisible by x - a . If we change a into a becomes x − ( − a ) = x + a ; also x " - a " becomes x " - ( -a ) ” , and x " − ( − a ) ” is x2 + a ” a " according as n is odd or even ...
Innhold
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a+b+c a₁ arithmetic mean arithmetical progression ax² b₁ binomial Binomial Theorem C₁ Cambridge coefficient contain continued fraction Crown 8vo denominator determinant digits divergent divide divisible divisor Edition equal equation ax example expansion Extra fcap Fcap Find the number Find the sum follows geometrical progression given expression Globe 8vo greater Hence the required infinity letters logarithm MACMILLAN'S Multiply negative nth convergent nth root nth term number of terms obtained P₁ periodic continued fraction positive integer powers prime number Professor prove quadratic equation quadratic surd quotient ratio remainder School Shew Solve the equation square root subtract suppose Theorem Trinity College u₁ unknown quantities white ball whole number zero
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