Question

The quotient of (x^4 - 3x^2 + 4x - 3) and the polynomial (x^2 + x - 3) is:

a) x^2 - 4x + 1
b) x^2 - 2x + 2
c) x^2 - 5x + 6
d) x^2 + 3x - 3

Answer 1

The quotient of (x^4 - 3x^2 + 4x - 3) and the polynomial (x^2 + x - 3) is x^2 - x + 7.

Step-by-step explanation:

To find the quotient of x^4 - 3x^2 + 4x - 3 divided by x^2 + x - 3, we can use polynomial division. Here are the steps:

1. Divide the first term of the numerator by the first term of the denominator: x^4 / x^2 = x^2.
2. Multiply the entire denominator by the result from step 1: (x^2 + x - 3) * x^2 = x^4 + x^3 - 3x^2.
3. Subtract the product from step 2 from the numerator: x^4 - 3x^2 + 4x - 3 - (x^4 + x^3 - 3x^2) = -x^3 + 7x - 3.

Therefore, the quotient is x^2 - x + 7.