Identifying the Degree and Leading Coefficient of a Polynomial Function

Identify the degree, leading term, and leading coefficient of the following polynomial functions.

\begin{matrix} f (x) & = & 3 + 2 x^{2} - 4 x^{3} \\ g (t) & = & 5 t^{5} - 2 t^{3} + 7 t \\ h (p) & = & 6 p - p^{3} - 2 \end{matrix}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
For the function $f (x),$ the highest power of $x$ is 3, so the degree is 3. The leading term is the term containing that degree, $−4 x^{3} .$ The leading coefficient is the coefficient of that term, $−4.$
For the function $g (t),$ the highest power of $t$ is $5,$ so the degree is $5.$ The leading term is the term containing that degree, $5 t^{5} .$ The leading coefficient is the coefficient of that term, $5.$
For the function $h (p),$ the highest power of $p$ is $3,$ so the degree is $3.$ The leading term is the term containing that degree, $- p^{3} .$ The leading coefficient is the coefficient of that term, $−1.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Identify the degree, leading term, and leading coefficient of the polynomial $f (x) = 4 x^{2} - x^{6} + 2 x - 6.$

How did it go?