Question

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.

Answer 1

Interpret the terms as 3x^5y, -2x^3y^4, -7xy^3 and -8x^5y, 2x^3y^4, xy^3.

Sum:
(3x^5y - 8x^5y) + (-2x^3y^4 + 2x^3y^4) + (-7xy^3 + xy^3)
= -5x^5y - 6xy^3,
highest total degree = 5+1 = 6.

Difference:
(3x^5y - (-8x^5y)) + (-2x^3y^4 - 2x^3y^4) + (-7xy^3 - xy^3)
= 11x^5y - 4x^3y^4 - 8xy^3,
highest total degree = 3+4 = 7.

So: The sum has degree 6, but the difference has degree 7.