To add the polynomials, combine like terms by adding the coefficients. The sum of the polynomials is 4x^3 - 3x^2 + x - 8.
To add the polynomials 3x^3+4x^2-x+8 and x^3-7x^2+2x-16, we combine like terms. We add the coefficients of the terms with the same degree of x.
Starting with the terms with degree 3, we have 3x^3 + x^3 = 4x^3.
Continuing with the terms with degree 2, we have 4x^2 - 7x^2 = -3x^2, and for the terms with degree 1, we have -x + 2x = x. Lastly, for the terms with degree 0 or the constant terms, we have 8 - 16 = -8.
Therefore, the sum of the polynomials is 4x^3 - 3x^2 + x - 8.
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