If f(x)=-2x³+x²+16x-15 and g(x)=x+3, we can substitute the polynomial in for f(x) and the binomial for g(x) like so:
[tex] \frac{2 x^{3}+ x^{2}+16x-15 }{x+3}[/tex]
The next step is to factor the numerator by grouping in the hopes that something will cancel!
[tex]\frac{(2 x^{3}+ x^{2}) +(16x-15) }{x+3} \\ \frac{ x^{2} (2x+1)+16x-15}{x+3} [/tex]
Unfortunately, because we can't factor anything out of the second grouped pair, that means there's no simplifying possible! So...
[tex] \frac{f(x)}{g(x)} = \frac{2 x^{3}+ x^{2} +16x-15 }{x+3}[/tex]
Hope this helps!
