Question

Given the polynomial 21x⁴ + 3y - 6x² - 34, what polynomial must be subtracted from it to obtain 29x² - 7? What polynomial must be added to it to obtain a first degree polynomial?

Answer 1

To obtain 29x² - 7, subtract 21x⁴ + 6x² - 3y + 41. To obtain a first degree polynomial, add a term that cancels out the degrees higher than one.

Step-by-step explanation:

To obtain 29x² - 7 from the polynomial 21x⁴ + 3y - 6x² - 34, we need to subtract the polynomial 21x⁴ + 6x² - 3y + 41. This gives us the desired polynomial.

To obtain a first degree polynomial from the given polynomial, we need to add a term that cancels out the degrees higher than one. Since the highest degree in the given polynomial is 4, we need to add a term of degree three and lower. For example, we can add the polynomial 2x³ + 4x - 7 to obtain a first degree polynomial.