Elementary Algebra for the Use of Preparatory Schools |
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Page 53
... positive or negative values . 57. Product of a Multinomial Expression and a Monomial . Consider the product ( a + b ) c , where a , b , and c have any values whatever . If c be a positive integer , and a and b have any values whatever ...
... positive or negative values . 57. Product of a Multinomial Expression and a Monomial . Consider the product ( a + b ) c , where a , b , and c have any values whatever . If c be a positive integer , and a and b have any values whatever ...
Page 54
... positive integer , ( a + b ) ÷ d = a ÷ d + b ÷ d . And since the operations of multiplication and division to be performed on a + b can be performed on a and b separately , this must also be the case for the complex m operation denoted ...
... positive integer , ( a + b ) ÷ d = a ÷ d + b ÷ d . And since the operations of multiplication and division to be performed on a + b can be performed on a and b separately , this must also be the case for the complex m operation denoted ...
Page 177
... positive integer , and xa divides a " - a " always , x + a x + a • ana " never , xn a " when n is even , - x2 + an . . . . odd . We have in the above shown that the four cases are all included in the first : we leave it as an exercise ...
... positive integer , and xa divides a " - a " always , x + a x + a • ana " never , xn a " when n is even , - x2 + an . . . . odd . We have in the above shown that the four cases are all included in the first : we leave it as an exercise ...
Page 178
... positive integer , 7 " — 1 is divisible by 6 ; show also that 352n + 1 + 1 is divisible by 36 . 11. Show without actual division that ( 3 x2 − 2 x + 1 ) 3 − ( 2 x2 + 3 x − 5 ) 3 is divisible by x2 - 5x + 6 . 12. Write down the result ...
... positive integer , 7 " — 1 is divisible by 6 ; show also that 352n + 1 + 1 is divisible by 36 . 11. Show without actual division that ( 3 x2 − 2 x + 1 ) 3 − ( 2 x2 + 3 x − 5 ) 3 is divisible by x2 - 5x + 6 . 12. Write down the result ...
Page 179
... positive integer . 16. Show that ( x − 1 ) 2 is a factor of nxn + 1 - ( n + 1 ) x2 + 1 , and also of xn ntn 1 , n being any positive integer . 148. Factor Theorem . If any rational and integral ex- pression which contains a vanish when ...
... positive integer . 16. Show that ( x − 1 ) 2 is a factor of nxn + 1 - ( n + 1 ) x2 + 1 , and also of xn ntn 1 , n being any positive integer . 148. Factor Theorem . If any rational and integral ex- pression which contains a vanish when ...
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7th term a²b a²b² a²x a²x² a³b ab² ab³ absolutely convergent algebraical expression arithmetic means ax² b₁ binomial theorem cents CHAPTER coefficients contain continued fraction convergent denote determinant difference digits Divide dividend division divisor equal equation x² example Find the factors Find the H. C. F. Find the number Find the square Find the sum Find the value finite formula geometrical progression given expression greater Hence indeterminate forms integer less letters limit logarithms monomial Multiply negative nth root number of terms obtain permutations positive integer powers Prove quadratic equation quotient remainder result Show Simplify simultaneous equations Solve the equation square root subtract surds unknown quantities x²y x²y² xy² xy³ zero
Popular passages
Page 46 - Multiplication is the process of taking one number as many times as there are units in another number.
Page 362 - Find the area of a circle whose radius is 12 feet, from the law that the area of a circle varies as the square of its radius.
Page 349 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 77 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 362 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".