The quotient of open paren x to the 4th power minus 3 x squared plus 4 x minus 3 close paren and open paren x squared plus x minus 3 close paren is a polynomial. What is the quotient?

Divide the leading terms: x⁴ ÷ x² = x², so the quotient starts with x². Subtracting x²(x² + x − 3) leaves −x³ + 4x − 3; dividing the leading terms again gives −x, and subtracting −x(x² + x − 3) leaves x² + x − 3. That is exactly the divisor, so the final quotient term is +1, giving x² − x + 1, choice A.

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