> Next up: what is the degree of our equation? The degree is the highest power of any term showing up. For example, if you have (a^2)b(c^4), that’s a term of degree 7 = 2 + 1 + 4
I thought that equation was degree 4, which aligns with what the author says later on. Am I missing something? It seems odd that he would write out that equation accidentally, maybe just crossed wires though. I'm sure we've all been there.
The wording in that paragraph is a bit confusing. In this context, "term" refers to the entire product, For example, the equation "(a^2)b + (b)c^4 = 0" has two terms: (a^2)b, and (b)c^4.
The degree of the entire equation is the maximum of the degree of the individual terms. However, the degree of a term is the sum of the degree of all of the factors.
For example, the equation "a+b+c=10" is degree 1, but "abc=10" is degree 3.
Ah ok so he was talking about the degree of the equation but gave an example of calculating the degree of a term, the highest of which in any equation is its degree. That makes sense, thanks for clearing it up!
The author defined degree poorly. a monomial x0^e0x1^e1...xn^en has degree e1+e2+...+en. A polynomial's degree is the highest degree of any of it's monomials.
Degree has the property that Deg(P1P2)=Deg(P1)Deg(P2)
If I understood your question correctly, you are saying that the degree of a term should be the maximum degree between the vatiables in that term. So (a^2)(b^1)(c^4) ) would be of degree max(2,1,4) = 4.
But with the definition he is using, the degree of a term in the equation is the sum of the degrees of the variables. So (a^2)(b^1)(c^4) has degree 2 + 1 + 4 = 7.
I don't think that's right. See the sibling comment, which made it click for me. He is saying the degree of a single term is the sum of the exponents in that term, and the degree of the equation is max(...all term degrees).
I thought that equation was degree 4, which aligns with what the author says later on. Am I missing something? It seems odd that he would write out that equation accidentally, maybe just crossed wires though. I'm sure we've all been there.