SOLUTION: This question is from the Oral Exercises section. I have to state degree of each polynomial. {I don't know how to type powers, so I apologize in advance for the poorly copied

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Question 126729This question is from textbook Algebra Structure and Method book 1
: This question is from the Oral Exercises section.
I have to state degree of each polynomial.
{I don't know how to type powers, so I apologize in advance for the poorly copied problem}
r{power of 2}s - 3rs{power of 3} + 2r{power of 3}s{power of 2} + s{power of 4}
My solution:
r= 2-1+3 = 4
s+ 1-3+2+4 + 4
Degree of polynomial is 8.
Back of book answer is 5.
Where did I go wrong? This question is from textbook Algebra Structure and Method book 1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
In the future, just use the ^ mark to denote raising to a power, like this:
r^2s-3rs^3+2r^3s^2+s^4.

r%5E2s-3rs%5E3%2B2r%5E3s%5E2%2Bs%5E4

To determine the degree of a polynomial, examine the degree of each of the monomial terms.

The degree of a monomial term is the sum of the exponents contained in the term:

r%5E2s is a degree 3 term because of the 2 exponent on the r and the 1 (understood) exponent on the s, and 2 + 1 = 3.

Find the term with the highest degree, and that is then the degree of the overall polynomial.

r%5E2s: Degree 3
-3rs%5E3: Degree 4
2r%5E3s%5E2: Degree 5
s%5E4: Degree 4

The highest degree term is the third term which is degree 5, therefore the degree of the polynomial is 5.