Question

which algebraic expression is a polynomial with a degree of 5? 2xy^{4}+4x^{3}y^{3}-6xy^{2}-7x^{4} 8y^{6}+y^{5}-5xy^{3}+7x^{2}y^{2}-x^{3}y-6x^{4} -6xy^{5}+5x^{2}y^{3}-x^{3}y^{2}+2x^{2}y^{3}-3xy^{5} 3x^{5}+8x^{4}y^{2}-9x^{3}y^{3}-6y^{5}

Explanation:

Step1: Recall polynomial degree rule

The degree of a polynomial in two variables is the highest sum of exponents of $x$ and $y$ in any single term.

Step2: Calculate degree for first expression

For $2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$:

• $2xy^4$: $1+4=5$; $4x^2y^3$: $2+3=5$; $-6x^3y^2$: $3+2=5$; $-7x^4$: $4$

Highest degree = 5

Step3: Calculate degree for second expression

For $8y^6 + y^5 - 5xy^3 + 7x^2y^2 - x^3y - 6x^4$:

• $8y^6$: $6$; $y^5$: $5$; others are lower.

Highest degree = 6

Step4: Calculate degree for third expression

For $-6xy^5 + 5x^2y^3 - x^3y^2 + 2x^2y^3 - 3xy^5$:

• $-6xy^5$: $1+5=6$; $-3xy^5$: $1+5=6$; others are lower.

Highest degree = 6

Step5: Calculate degree for fourth expression

For $3x^5 + 8x^4y^2 - 9x^3y^3 - 6y^5$:

• $8x^4y^2$: $4+2=6$; $-9x^3y^3$: $3+3=6$; others are lower.

Highest degree = 6

Answer:

$2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$