Question 1079594
7-x^3 is probably the one you're thinking of that has degree three. The degree is the largest exponent, which is 3. So this one is an answer.


However, there are others that may apply as well. It says "Select all that apply" implying that more than one answer is possible. Let's go through the list of choices


----------------------------------------------------------------------


Choice A) x^2yz+3yz^2 is NOT a degree 3 polynomial because the degree is actually 4. When it comes to multivariate polynomials (aka polynomials with more than one variable), you add up the exponents for each term. The first term x^2yz = x^2y^1z^1 has the exponents add up to 2+1+1 = 4. The second term exponents add up to 1+2 = 3. The largest sum here is 4, so the degree is 4.


Choice B) x^2y+3x+7y^2 is a polynomial of degree 3. The term x^2y, which is really x^2y^1 has the exponents add to 2+1 = 3. This is the largest sum so this is why the degree is 3. The other terms don't add up the exponents to 3.


Choice C) xyz is the same as x^1y^1z^1 and the exponents add to 1+1+1 = 3, making this another 3rd degree polynomial. The other terms don't add up the exponents to 3.


Choice D) is NOT an answer since the term xy has sum of exponents equal to 2 while z is simply with an exponent of 1.


Choice E) is a 3rd degree polynomial since the largest exponent is 3 for the term -x^3


-----------------------------------------------------------------------


In summary, the answers are: choice B, choice C, choice E