Elementary Algebra First Second Year Course volume 2

Cover Elementary Algebra First Second Year Course volume 2
Elementary Algebra First Second Year Course volume 2
Florian Cajori
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The sum of the same two even powers of two numbers may be factored, ifihe exponent is the product of an odd and an even factor. One factor is the sum of the numbers with exponents equal to the even factor ; the other factor may be found by inspection or by long division. Thus, in a 12 4 6 1 ' 2, the exponent 12 = 3 4, where 3 is odd, 4 even.
One factor of a 12 4 6 12 is a 4 4 6 4 . The other factor is a 8 a 4 6 4 + ft 8 .
Hence, a 12 + 6 12 =(a 4 4 6 4 )(a 8 - a 4 & 4 4 6 8 ).
If numerical cubi
...c equations of the form x 3 4 ax 2 4 bx + c = 0. A, b, c being positive or negative integers, have at least one root rational, then the equation can be solved with the aid of the Factor Theorem.
x 3 4 4 x 2 2x 5 becomes zero when 1 is substituted for x. Hence x 4- 1 is a factor, the quotient x 2 4 3 x 5 is another factor.
Write the cubic equation in the form (x 4 1) (x 2 4 3 x 5) = 0.
Make the first factor equal to zero, x 4- 1 = 0, and x = 1.
Make the second factor equal to zero, x 2 4 3 x 5 = 0, and solve the quadratic equation, x = .


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