Medals!
The quotient of (x^4 – 3x^2 + 4x – 3) and a polynomial is (x^2 + x – 3). What is the polynomial?

x^4 – 2x^2 + 5x – 6
x^2 – x + 1
x^6 + x^5 – 6x^4 + x^3 + 10x^2 – 15x + 9
x^4 – 4x^2 + 3x

Question

Medals!
The quotient of (x^4 – 3x^2 + 4x – 3) and a polynomial is (x^2 + x – 3). What is the polynomial?

x^4 – 2x^2 + 5x – 6
x^2 – x + 1
x^6 + x^5 – 6x^4 + x^3 + 10x^2 – 15x + 9
x^4 – 4x^2 + 3x

anonymous · Answer

$$
x^2+x-3 = \frac{x^4 – 3x^2 + 4x – 3}{p(x)}
$$So: $$
p(x)[x^2+x-3] = x^4 – 3x^2 + 4x – 3
$$

anonymous · Answer

Also $$
p(x) = \frac{x^4 – 3x^2 + 4x – 3}{x^2 + x – 3}
$$

anonymous · Answer

So you divide the dividend by the quotient to find the divisor?

anonymous · Answer

Hello? You there?