Question

Which algebraic expression is a polynomial with a degree of 5?

3x5 + 8x4y2 – 9x3y3 – 6y5
2xy4 + 4x2y3 – 6x3y2 – 7x4
8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4
–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5

Answer 1

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

Explanation:

Since, the highest degree in a polynomial is called the degree of the polynomial,

While, the degree of each term in a polynomial with two variables is the sum of the exponents in each term.

In
`3x^5 + 8x^4y^2 - 9x^3y^3 - 6y^5`,

Sum of exponents are 5, 6, 6, 5,

So, degree of the polynomial is 6.

In
`2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4`,

Sum of exponents are 5, 5, 5, 4,

So, degree of the polynomial is 5.

In
`8y^6 + y^5 - 5xy^3 + 7x^2y^2 - x^3y - 6x^4`,

Sum of exponents are 6, 5, 4, 4, 4, 4

So, degree of the polynomial is 6.

In
`-6xy^5 + 5x^2y^3 - x^3y^2 + 2x^2y^3 -3xy^5`,

Sum of exponents are 6, 5, 5, 5, 5

So, degree of the polynomial is 6.

Answer 2

The degree of a polynomial is the highest exponent or sum of exponents of the variables in the individual terms of a polynomial.

Looking at each the polynomial:

3x5 + 8x4y2 – 9x3y3 – 6y5: Degree is 6 (look at the 2nd and 3rd term)

2xy4 + 4x2y3 – 6x3y2 – 7x4: Degree is 5 (look at 1st, 2nd, and 3rd term)

8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4: Degree is 6 (look at 1st term)

–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5: Degree is 6 (look at 1st and last term)

Therefore, the answer is the second option:
2xy4 + 4x2y3 – 6x3y2 – 7x4