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Answer :
Final answer:
To add the polynomials (8x⁴ + 9x³ + 10x) and (10x⁴ + 3x³ - 10), you combine like terms resulting in the sum 18x⁴ + 12x³ + 10x - 10.
Explanation:
To add the two polynomials (8x⁴ + 9x³ + 10x) + (10x⁴ + 3x³ - 10), we combine like terms, which means adding coefficients of the terms with the same exponent. We add the coefficients of x⁴ terms, the x³ terms, and the constant terms separately.
The sum of the coefficients of the x⁴ terms: 8 + 10 = 18.
The sum of the coefficients of the x³ terms: 9 + 3 = 12.
Since there are no x² or x terms in the second polynomial, the 10x term remains unchanged, and we simply add the constant terms: 0 + (-10) = -10.
The final sum of the two polynomials is 18x⁴ + 12x³ + 10x - 10.
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