Intermediate/Advanced Factoring

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
missmorgan
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Intermediate/Advanced Factoring

Postby missmorgan » Wed Sep 07, 2011 6:36 am

I know I've done things like this before, but I don't have my book on hand and I've forgotten quite a bit over summer. I've been looking online and can't find any problems similar to this. :/ Help please?

1. Factor Image

2. Factor Image

For number two I got an answer of (x+7)^1/4[1+(x+7)^1/2]... but I'm still a little uncomfortable with the whole way I did it.

(x+7)^1/4+(x+7)^1+1/4
(x+7)^1/4+(x+7)*(x+7)^-1/4
(x+7)^1/4[1+(x+7)(x+7)^-1/4-1/4]
(x+7)^1/4[1+(x+7)(x+7)^-1/2]
(x+7)^1/4[1+(x+7)^1/2]

nona.m.nona
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Re: Intermediate/Advanced Factoring

Postby nona.m.nona » Wed Sep 07, 2011 12:10 pm

missmorgan wrote:1. Factor

It might help to convert to a common denominator, combine, and then rationalize the denominator.



Note also that a "2" may be factored out.

missmorgan wrote:2. Factor

For number two I got an answer of (x+7)^1/4[1+(x+7)^1/2]... but I'm still a little uncomfortable with the whole way I did it.

(x+7)^1/4+(x+7)^1-1/4
(x+7)^1/4+(x+7)*(x+7)^-1/4
(x+7)^1/4[1+(x+7)(x+7)^-1/4-1/4]
(x+7)^1/4[1+(x+7)(x+7)^-1/2]
(x+7)^1/4[1+(x+7)^1/2]

It might "feel" better to convert 3/4 into 1/2 + 1/4, rather than into 1 - 1/4. But the result should be the same.


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