which algebraic expression is a polynomial with a degree of 5?\n3x^5 + 8x^4y^2 - 9x^3y^3 - 6y^5\n2xy^4 +…

Explanation:

Step1: Recall degree of a polynomial in two - variables

The degree of a term in a polynomial in two variables (x) and (y) is the sum of the exponents of (x) and (y) in that term, and the degree of the polynomial is the highest degree of its terms.

Step2: Analyze the first option

For the polynomial (3x^{5}+8x^{4}y^{2}-9x^{3}y^{3}-6y^{5}), the degree of (3x^{5}) is 5, the degree of (8x^{4}y^{2}) is (4 + 2=6), the degree of (-9x^{3}y^{3}) is (3+3 = 6), the degree of (-6y^{5}) is 5. The highest degree is 6.

Step3: Analyze the second option

For the polynomial (2xy^{4}+4x^{2}y^{3}-6x^{3}y^{2}-7x^{4}), the degree of (2xy^{4}) is (1 + 4=5), the degree of (4x^{2}y^{3}) is (2+3 = 5), the degree of (-6x^{3}y^{2}) is (3 + 2=5), the degree of (-7x^{4}) is 4. The highest degree is 5.

Step4: Analyze the third option

For the polynomial (8y^{6}+y^{5}-5xy^{3}+7x^{2}y^{2}-x^{3}y - 6x^{4}), the degree of (8y^{6}) is 6, the degree of (y^{5}) is 5, the degree of (-5xy^{3}) is (1+3 = 4), the degree of (7x^{2}y^{2}) is (2 + 2=4), the degree of (-x^{3}y) is (3+1 = 4), the degree of (-6x^{4}) is 4. The highest degree is 6.

Step5: Analyze the fourth option

For the polynomial (-6xy^{5}+5x^{2}y^{3}-x^{3}y^{2}+2x^{2}y^{3}-3xy^{5}), the degree of (-6xy^{5}) is (1+5 = 6), the degree of (5x^{2}y^{3}) is (2 + 3=5), the degree of (-x^{3}y^{2}) is (3+2 = 5), the degree of (2x^{2}y^{3}) is (2+3 = 5), the degree of (-3xy^{5}) is (1+5 = 6). The highest degree is 6.

Answer:

(2xy^{4}+4x^{2}y^{3}-6x^{3}y^{2}-7x^{4})