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

1 Answer
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).