Let and be polynomials. Find if the degree of is and the degree of is .

Question

Let  and  be polynomials. Find  if the degree of  is  and the degree of  is  .

Quizplus · Accepted Answer

The degree of the sum or difference of two polynomials is equal to the degree of the polynomial with the highest degree. Since the degree of 11eaa3e5_55ca_e592_9f8f_0f3d22789cbd_TB5971_11 is greater than the degree of both given polynomials, we can ignore the leading terms of both polynomials. So, we have:
11eaa3e5_55ca_be80_9f8f_8952eb254529_TB5971_11 - 11eaa3e5_55ca_be81_9f8f_79ce0b02ede1_TB5971_11 = 11eaa3e5_55ca_5aca_9f8f_8f4c7a51e54e_TB5971_11
Ignoring the leading terms of this result (which are equal), we have:
11eaa3e5_55ca_e592_9f8f_0f3d22789cbd_TB5971_11 = 11eaa3e5_55ca_5aca_9f8f_8f4c7a51e54e_TB5971_11 + 11eaa3e5_55ca_be81_9f8f_79ce0b02ede1_TB5971_11
Now, the leading term of 11eaa3e5_55cb_0ca5_9f8f_5971f488f14e_TB5971_11 is x^3, and the degree of the sum of the two polynomials should be 11eaa3e5_55ca_e594_9f8f_098e62a043f4_TB5971_11+3=11eaa3e5_55ca_e597_9f8f_afa6a914c6dd_TB5971_11. Therefore, the leading term of 11eaa3e5_55cb_0ca5_9f8f_5971f488f14e_TB5971_11 should be 11eaa3e5_55ca_33b4_9f8f_7ad1e178923f_TB5971_11. So, ignoring the leading terms of both polynomials, we have:
11eaa3e5_55ca_e592_9f8f_0f3d22789cbd_TB5971_11 + 11eaa3e5_55cb_0ca5_9f8f_5971f488f14e_TB5971_11 = 11eaa3e5_55ca_33b4_9f8f_ea60d42fcefb_TB5971_11
Therefore, the answer is D.

Let and Be Polynomials