# Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following :

Question : Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following :

(i)  p(x) = $$x^3 – 3x^2 + 5x – 3$$,  g(x) = $$x^2 – 2$$

(ii)  p(x) = $$x^4 – 3x^2 + 4x + 5$$, g(x) = $$x^2 + 1 – x$$

(iii)  p(x) = $$x^4 – 5x + 6$$,  g(x) = $$2 – x^2$$

Solution :

(i)  Here, dividend and divisor are both in standard forms. So, we have :

$$\therefore$$  The quotient is x – 3 and the remainder is 7x – 9

(ii)  Here, dividend is already in standard form and the divisor is not in the standard form. It can be written as $$x^2 – x + 1$$. We have :

$$\therefore$$  The quotient is $$x^2 + x – 3$$ and the remainder is 8.

(iii) Here, dividend and divisor are both in standard forms. So, we have :

$$\therefore$$  The quotient is $$-x^2 – 2$$ and the remainder is -5x + 10.