Please help with problem

Question

What are the leading coefficient and degree of the polynomial?

-18v + 20v^6 - 10 + 23v^4

Answer 1

Hi Jane S.,

Degree is the number of the highest exponent, here = 6 . Leading coefficient = coefficient of the first term of the polynomial when (re-)written in standard form, i.e. 20v^6 +23v^4 -18v -10 . So "20".

Those are just definitions. But they point up the desirability of writing the polynomial in standard form, because you may then start to preceive groupings of terms which may enable you to factor it into products of terms.

That's always useful, because you can then (possibly) get some exact expressions for zeros of the polynomial written down. And since polynomials are used in equations which describe real-world problems, especially in the equation type:

"Polynomial = 0"

you can then get exact answers to the problem!

-- Cheers, -- Mr. d.

Answer 2

To get the leading degree and coefficient, we will want to order the monomial terms into "greatest to least" format...

In this case the original problem shows : -18v + 20v⁶ - 10 + 23v⁴

Reordering these terms (under the additivity priniciple) gives us : 20v⁶ + 23v⁴ - 18v - 10

Now we can read off the highest (leading) degree which is v to the power of 6 (v⁶) and its coefficient is 20.