Question

A polynomial function may have zero, one, or many zeros. All polynomial functions of positive, odd order have at least one zero, while polynomial functions of positive, even order may not have a zero.

Answer 1

`\begin{gathered} a)-10x^{3\text{ }}+16x^2\text{ + 16x - 12} \\ \text{This example is and even order so it could not have zeros.} \end{gathered}`

All posible zeros for the first exercise are: -1, + 1, -2, +2, -3, +3, -4, +4, -6, -6, -12, +12, - 5/6, +6/5, -6/5.

Synthetic division is useful to find the possible roots to find the exact roots in an quick way.

3.- Yes, it's possible. Zeros are when a polynomial crosses the x-axis. Some polynomials do not cross this axis so there will not be roots.

4.-

`\begin{gathered} \text{ 0= -16t}^2\text{ + vot + }5 \\ 0=-16t^2\text{ + 300t + }5 \\ -16t^2\text{ + 300t + 5 = 0} \\ \end{gathered}`

It isn't possible to factor this polynomial.