Question

f(x)=x^3+6x^2+x^1/2 and g(x)+x^1/2 . find f(x) divided by g(x)

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that $f(x)=x^{3}+6x^{2}+x^{\frac{1}{2}}$ and $g(x)=x^{\frac{1}{2}}$, therefore, you must divide must fucntion, as following:

$\frac{f(x)}{g(x)}=\frac{x^{2}+6x^{2}+x^{\frac{1}{2}}}{x^{\frac{1}{2}}}$

2. You must simplify it,by factoring out $x^{\frac{1}{2}}$, as following:

$\frac{f(x)}{g(x)}=\frac{x^{\frac{1}{2}}( x^{\frac{5}{2}}+6x^{\frac{3}{2}}+1)}{x^{\frac{1}{2}}}$

3. Finally, you obtain that the answer is:

$\frac{f(x)}{g(x)}= x^{ \frac{5}{2} } +6 x^{ \frac{3}{2} } +1$