Question

I am clueless about classifying polynomials by degree and number of terms. What kind of help can you give me?

Answer 1

Whenever there's an interruption of say a sign like + or -, what's before it and after it is a "term", so for example,

a + b  <---- two terms

a + b + c <---- three terms

25x⁻¹ - 17y² + 3 - 21x²    <---- four terms.

the degree of a polynomial, is based on the exponents of the variables in each term, you add the exponents of the variables for that term, and the term with the highest degree, is the degree of the polynomial,

$\bf 17x^2y^3z^7~+~3x^8~-~21z^9~+~100x^3y^8$

notice the polynomial here, it has 4 terms... what's its degree?  let's check the degree of each term,

$\bf \begin{cases} 17x^2y^3z^7\impliedby &2+3+7\\ &de gree~12\\ 3x^8\impliedby &8\\ &de g ree~8\\ 21z^9\impliedby &9\\ &de g ree~9\\ 100x^3y^8\impliedby &3+8\\ &de g ree~11 \end{cases}$

the term with the highest degree is the first one, with 12, and therefore, the degree of that polynomial is 12 then.