Question

How do you find the degree, leading term, the leading coefficient, the constant term and the end behavior of `p(t)=-t^2(3-5t)(t^2+t+4)`?

Answer 1

If we multiply all of the parts together, we can see that the highest order term will be when we multiply the `-t^2` with the `-5t` and the `t^2`, so it will be a term that looks like `5t^5`. That gives us the degree (5 in the exponent), the leading term (`5t^5`), the leading coefficient (5) and the end behavior (more about that in a second). The constant term will be 0 because every term gets multiplied by `t^2` so there is no constant term.

The end behavior for a polynomial is always the leading term. For very high values of `t`, the `5t^5` will be much larger than any of the other terms.