Final answer:
To find the sum of the given polynomials, add the like terms in both polynomials. The resulting polynomial is the sum of all these terms: 4x4 + 6x3 + 2x2 + 10x + 17.
Step-by-step explanation:
The method to determine the sum of the polynomials (x4 + 6x3 + 10x + 5) and (3x4 + 2x2 + 12) involves adding the like terms from both the polynomials together. Like terms are terms that have the same variables raised to the same power. Here in these polynomials, you can add the coefficients of like terms.
For the x4 terms, add x4 from the first polynomial and 3x4 from the second to get 4x4. Similarly, for the x3 terms, you have 6x3 in the first polynomial and no x3 term in the second polynomial. So you simply carry over 6x3.
Proceed this way with the rest of the terms. The final answer will be the sum of all these terms: 4x4 + 6x3 + 2x2 + 10x + 17.
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