Which sum represents the partial fraction decomposition of the fraction with numerator 8 x to the 4th power plus 3 x cubed minus 115 x squared minus 39 x plus 200 and denominator 3 x open paren x squared plus 10 close paren squared ?

The denominator has a linear factor, x, and a repeated irreducible quadratic factor, (x² + 10)². The partial fraction form uses a constant numerator over x, then a linear numerator over each power of the quadratic: A/x + (Bx + C)/(x² + 10) + (Dx + E)/(x² + 10)². The factor 3 can be absorbed into the unknown coefficients, so choice A has the correct form.

AI-written and checked against the verified answer.