Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3?
Both the sum and difference have a degree of 6.
Both the sum and difference have a degree of 7.
The sum has a degree of 6, but the difference has a degree of 7.
The sum has a degree of 7, but the difference has a degree of 6.
The degree of a polynomial is determined by the highest exponent of any term in the polynomial.
In this case, the highest exponent of any term in the polynomials 3x^5y - 2x^3y^4 - 7xy^3 and -8x^5y + 2x^3y^4 + xy^3 is 5 for the term 3x^5y and -8x^5y, respectively.
The sum of the two polynomials is (3x^5y - 2x^3y^4 - 7xy^3) + (-8x^5y + 2x^3y^4 + xy^3) = -5x^5y + 0x^3y^4 - 6xy^3.
The highest exponent in this sum is 5 for the term -5x^5y, so the degree of the sum is 5.
The difference of the two polynomials is (3x^5y - 2x^3y^4 - 7xy^3) - (-8x^5y + 2x^3y^4 + xy^3) = 11x^5y - 4x^3y^4 - 8xy^3.
The highest exponent in this difference is also 5 for the term 11x^5y, so the degree of the difference is 5.
Therefore, both the sum and difference have a degree of 5. None of the given options are correct.