How do you write the rational expression #(x^3+5x^2+6x)/x^-4# in simplest form?

1 Answer
Massimiliano · Sidharth
Feb 3, 2015

The answer is: #x^7+5x^6+6x^5#, simply remembering that:

#1/x^-4=x^4#, and so:

#(x^3+5x^2+6x)/x^-4=(x^3+5x^2+6x)x^4=x^7+5x^6+6x^5=x^5(x^2 + 5x + 6)=x^5(x+2)(x+3)#.

This is because I found the two numers whose sum is #5# and whose product is #6# (#a=1#, #b=5# and #c=6#, if #a!=1# another way to factor has to be used).

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