Answer:
[tex]s=5t^{3}-10t^{2}-10t-20+\frac{46}{t+2}[/tex]
Step-by-step explanation:
To find answer, we have to use the relation of the movement
[tex]d=st[/tex]
Where, the speed would be
[tex]s=\frac{d}{t}[/tex]
Now, the given expressions are about distance and time, if we replace this expression in the formula above, we would have to divide both polynomials as follows
[tex]s=\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]
If we divide, we would have a long division as it's attached. And the result would be
[tex]s=5t^{3}-10t^{2}-10t-20+\frac{46}{t+2}[/tex]
Because according to Euclid's algorithm:
[tex]\frac{D}{d}=q+r[/tex]
So, the fraction at the end, it's because the division is not exact, that is, the reminder is different than zero.
