Consider the polynomial given below pt t65 9tt2 t 2 Find

Consider the polynomial given below. p(t) = -t^6(5 - 9t)(t^2 + t + 2) Find the degree.

Solution

p(t)= -t⁶(5-9t)(t² + t+2)

degree

Here we have t⁶,t and t²= t⁹

The degree is 9

leading terms

If we multiply all of them we get

p(t)=9t⁹+4t⁸+13t⁷-10t⁶

The leading term is 9t⁹

leading coefficient is 9

End behaviour

The degree is odd, and the leading coefficient is +ve, in this case

when t->infinity, f(t)-> +infinity

t->-infinity, f(t)-> -infinity