Question

Which algebraic expression is a polynomial with a degree of 5? 3x5 8x4y2 â€"" 9x3y3 â€"" 6y5 2xy4 4x2y3 â€"" 6x3y2 â€"" 7x4 8y6 y5 â€"" 5xy3 7x2y2 â€"" x3y â€"" 6x4 â€""6xy5 5x2y3 â€"" x3y2 2x2y3 â€"" 3xy5.

Answer 1

Option 2  : $2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$ is the needed polynomial with the degree 5.

Given polynomials are:

$3x^5 + 8x^4y^2 -9x^3y^3 - 6y^5\\2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4\\8y^6 + y^5 - 5xy^3 + 7x^2y^2 - x^3y - 6x^4\\-6xy^5 + 5x^2y^3 - x^3y^2 + 2x^2y^3 - 3xy^5$

Explanation:

A polynomial is called to be of degree x when the maximum of respective total powers of each term is valued as x.

Thus the polynomial is called to be of degree 5 when its maximum power would be 5.

Power of a term in polynomial is calculated by summing the powers of all variables present in that term.

Option 1 has maximum power(degree) as 6

Option 2 has maximum power (degree)  of 5

Option 3 has maximum power (degree)  of 6

Option 4 also has maximum power (degree)  of 6.

Thus option 2  : $2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$ is the needed polynomial with the degree 5.

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