Identifying the Degree and Leading Coefficient of a Polynomial

For the following polynomials, identify the degree, the leading term, and the leading coefficient.

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.

1
Solution
1. ⓐ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, $−4.$
2. ⓑ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, $5.$
3. ⓒ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 $4 x^{2} - x^{6} + 2 x - 6.$

How did it go?