Posted by Z32 on Thursday, September 17, 2009 at 7:56pm.
I wanted to know how you would know that 4x^2 + 2x +90 / x5 would be able to factor down to (x5)(4x18)/x5
By looking at 4x^2 + 2x +90 / x5 , I would never think that it could be factored down to (x5)(4x18)/x5
How should I approach it so I know that it could be factored down to (x5)(4x18)/x5?

Calculus  MathMate, Thursday, September 17, 2009 at 8:18pm
First you take out common factors.
4x^2 + 2x +90 = 2(2x²x45)
Is it possible to find a, b such that ab=45, 2a+b=1 or a+2b=1?
Look at the factors of the constant term, namely 45=5*9. Since 2*59=1, we can try the factors 5 and 9 in different ways to get:
(2x+9)(x5)

Calculus  Reiny, Thursday, September 17, 2009 at 8:20pm
rather hard to explain in detail here.
this page
http://www.recitfga.qc.ca/english/activities/sitsat2006/jeanfoster/03.htm
gives a reasonable explanation.
I became suspicious when I saw the simple factor x5 in the denominator, and had a sneaking suspicion that it could also be in the top.
so I subbed in x=5 into the top and sure enough, I got a zero for the result.
(recall the factor theorem, which says that if f(a) = 0 then xa is a factor)
so I know that
4x^2 + 2x +90
= (x  5)(?x ± ?)
now a bit of logic,
what multiplied by x would give me 4x^2 ? , clearly 4x
what multiplied by 5 would give me +90 ? clearly 18
so
4x^2 + 2x +90 = (x5)(4x18)
BTW, the answer can be taken further by dividing out the x5 and simplifying the top
(x5)(4x18)/x5
= 2(2x + 9), x cannot be equal to 5
Answer This Question
Related Questions
 Science  If you lost your ability to feel (your sense of touch) would to still ...
 Science question, only 1  What would be the consequence of an ecosystem that ...
 Science  3. Which factor below helps species avoid extinction? A. Low ...
 Basic Math  How would I be able t find how many cubic centimeters in a cubic ...
 4th Grade Math  Re: Factor Numbers My son has to write at least two ways to ...
 4th Grade Math  Re: Factor Numbers My son has to write at least two ways to ...
 socials  this is the same question I posted yesterday, it is due tommorow, oh ...
 Liberal Arts Math  how would i solve this problem?? it says factor the ...
 Grammar  The accident........if the motorist had obeyed the speed limit. A. ...
 algebra  this is what u do on your first problem....first u take out the ...
More Related Questions