# Divide the polynomial p(x) = x^{3} - 3x^{2} + 5x - 3 by the polynomial g(x) = x^{2} - 2. Find the quotient and remainder.

**Solution:**

Let p(x) and g(x) be any polynomial of degree greater than or equal to one.

Let p(x) = x^{3} - 3x^{2} + 5x - 3; g(x) = x^{2} - 2.

We will use the long division method to find the quotient and remainder of the polynomial p(x) when divided by g(x).

Divisibility Check:

Dividend = Divisor × quotient + remainder

x^{3} - 3x^{2} + 5x - 3 = (x^{2} - 2) × (x - 3) + (7x - 9)

x^{3} - 3x^{2} + 5x - 3 = (x^{3} - 3x^{2} - 2x + 6) + (7x - 9)

x^{3} - 3x^{2} + 5x - 3 = x^{3} - 3x^{2} + 5x - 3

LHS = RHS

Hence by using the long division method, the quotient and remainder of the polynomial p(x) = x^{3} - 3x^{2} + 5x - 3 when divided by the polynomial g(x) = x^{2} - 2 are x - 3 and 7x - 9 respectively.

## Divide the polynomial p(x) = x³ - 3x² + 5x - 3 by the polynomial g(x) = x² - 2. Find the quotient and remainder.

**Summary:**

The quotient and remainder when x^{3} - 3x^{2} + 5x - 3 is divided by the polynomial g(x) = x^{2} - 2 are x - 3 and 7x - 9 respectively.