Algebra for Beginners |
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Page 20
... remainder to the sum of 4pq - p2 - 3q2 and 2p2 + 6q2 . 21. Subtract 3b3 + 2b2-8 from zero , and add the result to b4-263 + 3b . 22. By how much does the sum of 2m3 - 2m3 +5 , 3m3 + 4m2 + 5m + 3 , fall short of m3 + 2m - 1 , m2 - 3m ...
... remainder to the sum of 4pq - p2 - 3q2 and 2p2 + 6q2 . 21. Subtract 3b3 + 2b2-8 from zero , and add the result to b4-263 + 3b . 22. By how much does the sum of 2m3 - 2m3 +5 , 3m3 + 4m2 + 5m + 3 , fall short of m3 + 2m - 1 , m2 - 3m ...
Page 36
... remainder 4x2- 3 . In all cases where the division is not exact , the work should be carried on until the highest power in the remainder is lower than that in the divisor . 53. Occasionally it may be found convenient to arrange the ...
... remainder 4x2- 3 . In all cases where the division is not exact , the work should be carried on until the highest power in the remainder is lower than that in the divisor . 53. Occasionally it may be found convenient to arrange the ...
Page 48
... alphabetically ; thus in the first , remainder a b precedes a'c , and ac precedes 3abc . A similar arrangement will be observed throughout the work . 67. The following examples in division may be easily veri- 48 [ CHAP . ALGEBRA .
... alphabetically ; thus in the first , remainder a b precedes a'c , and ac precedes 3abc . A similar arrangement will be observed throughout the work . 67. The following examples in division may be easily veri- 48 [ CHAP . ALGEBRA .
Page 52
... are equal . If from equals we take equals the remainders are equal . 3. If equals are multiplied by equals the products are equal . 4 . If equals are divided by equals the quotients are equal . 75. Consider the equation 7x = 14 . It is.
... are equal . If from equals we take equals the remainders are equal . 3. If equals are multiplied by equals the products are equal . 4 . If equals are divided by equals the quotients are equal . 75. Consider the equation 7x = 14 . It is.
Page 63
... remainder c . 22. What is the remainder if x divided by y gives a quotient z ? 23. What is the quotient if when m is divided by n there is a remainder r ? 24. If a bill is shared equally among n persons , and each pays 75 cents , how ...
... remainder c . 22. What is the remainder if x divided by y gives a quotient z ? 23. What is the quotient if when m is divided by n there is a remainder r ? 24. If a bill is shared equally among n persons , and each pays 75 cents , how ...
Common terms and phrases
a²+b² acres algebraical sum Arithmetic arranged beginner cents CHAPTER coefficient Completing the square compound expressions convenient cube root descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII exceeds Find the highest Find the lowest find the number Find the product Find the square Find the sum find the value following expressions given expressions half-dollars Hence highest common factor lowest common denominator lowest common multiple lowest terms miles an hour miles per hour minute-hand Multiply negative numerator and denominator obtain quadratic equation quotient Reduce to lowest remainder removing brackets Resolve into factors result rule of signs side simple equation simultaneous equations Solve the equations square root Subtract Transposing trinomial unknown quantities walk whence write yards α α
Popular passages
Page 91 - The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal to the square of the first plus twice the product of the first by the second, plus the square of the second.
Page 107 - Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Page 89 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 54 - Transpose all the terms containing the unknown quantity to one side of the equation, and the "known quantities to the other.