polynomial

Question

For the following polynomial: 6a^2-7+2a^8 What is the degree of each term. Determine the leading term and the leading coefficient. Determine the degree of the polynomial.

Answer 1

I gave you an example of this in your previous question, so you should be able to determine the polynomial's degree. One thing that might give you trouble is the term -7. Since there's no variable there, it might be hard to figure out that term's degree. But think about this:

 

-7x⁰ = -7(1) = -7,

 

since anything raised to the 0 power is 1. So, you can imagine that that term is actually -7x⁰, which is why we say it has a degree of 0.

 

 

In terms of the leading coefficient, that's just the number stuck on the front of your leading term, ie., the term with the highest degree. In the polynomial 5x³ - 9x⁴ - 2x² + 7, the leading term is -9x⁴ (since it has the highest degree), so the leading coefficient is -9.