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.

Answer 1

Hi,

The sum has a degree of 6, but the difference has a degree of 7.

Explanation:

`P_1(x,y)=-2x^3y^4+3x^5y-7xy^3\ has\ degree\ =7\\\\P_2(x,y)=2x^3y^4-8x^5y+xy^3 \ has\ degree\ =7\\\\P_1+P_2=-5x^5y-6xy^3 \ has\ degree\ =6\\\\P_1-P_2=-4x^3y^4+11x^5y -8xy^3 \ has\ degree\ =7\\\\`