Question

What is the leading term, leading coefficient, and degree of this polynomial `-a + 8a^3 - 4a^7 + 4a^2`?

Answer 1

See below:

Explanation:

Let's rearrange this polynomial to standard form with descending degree. We now have

`-4a^7+8a^3+4a^2-a`

The leading term is simply the first term. We see that this is `-4a^7`.

The leading coefficient is the number in front of the variable with the highest degree. We see that this is `-4`.

The degree of a polynomial is simply the sum of the exponents on all terms.

Recall that `a=a^1`. Summing up the degrees, we get

`7+3+2+1=13`

This is a `13`th degree polynomial.

Hope this helps!