The quotient of (x5 – 3x3 – 3x2 – 10x + 15) and (x2 – 5) is a polynomial. What is the quotient?

Check the proposed quotient by multiplying it by the divisor: (x² − 5)(x³ + 2x − 3) = x⁵ + 2x³ − 3x² − 5x³ − 10x + 15. Combining like terms gives x⁵ − 3x³ − 3x² − 10x + 15, which matches the dividend exactly. Therefore, the quotient is x³ + 2x − 3, choice C.

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