High School

Stefan evaluated the sum of the polynomials \(3x^4 - 6x^2 - 4x - 9\) and \(x^4 - 3x^2 - 10x + 2\). What is the simplified form of the sum?

a) \(4x^4 - 9x^2 - 14x - 7\)
b) \(4x^4 - 9x^2 + 14x - 7\)
c) \(4x^4 - 9x^2 + 14x + 7\)
d) \(4x^4 - 9x^2 - 14x + 7\)

Answer :

Final answer:

The simplified form of the sum is 8x⁴−3x²−14x−7.

Explanation:

The simplified form of the sum is 8x⁴−3x²−14x−7 (option d).



To find the sum of the polynomials, we add the corresponding terms. The sum of the constant terms is -9 + 2 = -7. The sum of the x terms is -4x - 10x = -14x. The sum of the x² terms is -6x² - 3x² = -9x². The sum of the x⁴ terms is 3x⁴ + x⁴ = 4x⁴.



Therefore, the simplified form of the sum is 4x⁴ - 9x² - 14x - 7 (option d).

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