QuestionAugust 27, 2025

Which is true about the degree of the sum and difference of the polynomials 3x^5y-2x^3y^4-7xy^3 and -8x^5y+2x^3y^4+ 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.

Which is true about the degree of the sum and difference of the polynomials 3x^5y-2x^3y^4-7xy^3 and -8x^5y+2x^3y^4+ 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.
Which is true about the degree of the sum and difference of the polynomials 3x^5y-2x^3y^4-7xy^3 and -8x^5y+2x^3y^4+
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.

Solution
4.3(306 votes)

Answer

Both the sum and difference have a degree of 6. Explanation 1. Identify the degree of each polynomial The degree is determined by the highest sum of exponents in a term. For 3x^{5}y, the degree is 5+1=6. For -8x^{5}y, the degree is also 6. 2. Calculate the degree of the sum Sum: (3x^{5}y - 2x^{3}y^{4} - 7xy^{3}) + (-8x^{5}y + 2x^{3}y^{4} + xy^{3}) = -5x^{5}y + 0x^{3}y^{4} - 6xy^{3}. The highest degree term is -5x^{5}y, degree 6. 3. Calculate the degree of the difference Difference: (3x^{5}y - 2x^{3}y^{4} - 7xy^{3}) - (-8x^{5}y + 2x^{3}y^{4} + xy^{3}) = 11x^{5}y - 4x^{3}y^{4} - 8xy^{3}. The highest degree term is 11x^{5}y, degree 6.

Explanation

1. Identify the degree of each polynomial<br /> The degree is determined by the highest sum of exponents in a term. For $3x^{5}y$, the degree is $5+1=6$. For $-8x^{5}y$, the degree is also $6$.<br /><br />2. Calculate the degree of the sum<br /> Sum: $(3x^{5}y - 2x^{3}y^{4} - 7xy^{3}) + (-8x^{5}y + 2x^{3}y^{4} + xy^{3}) = -5x^{5}y + 0x^{3}y^{4} - 6xy^{3}$. The highest degree term is $-5x^{5}y$, degree $6$.<br /><br />3. Calculate the degree of the difference<br /> Difference: $(3x^{5}y - 2x^{3}y^{4} - 7xy^{3}) - (-8x^{5}y + 2x^{3}y^{4} + xy^{3}) = 11x^{5}y - 4x^{3}y^{4} - 8xy^{3}$. The highest degree term is $11x^{5}y$, degree $6$.
Click to rate: