which algebraic expression is a polynomial with a degree of 5?\n$3x^{5}+8x^{4}y^{2}-9x^{3}y^{3}-6y^{5}$\n$2xy…

Explanation:

Step1: Recall degree of a term in polynomial

The degree of a term (ax^{m}y^{n}) in a polynomial in two - variables (x) and (y) is (m + n), and the degree of a 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), and 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), and 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), and 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), and 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})