Question

The quotient of (x4 – 3x2 + 4x – 3) and (x2 + x – 3) is a polynomial. What is the quotient?
x4 – 2x2 + 5x – 6
x2 – x + 1
x6 + x5 – 6x4 + x3 + 10x2 – 15x + 9
x4 – 4x2 + 3x

Answer 1

x^2 − x + 1

Reason: Let the quotient be ax^2+bx+c. Multiplying by x^2+x−3 and equating coefficients to x^4−3x^2+4x−3 gives a=1, b=−1, c=1, so the quotient is x^2−x+1.