Divide the polynomial x³ – 3x² + 5x – 3 by x² – 2

Question

Q. Divide the polynomial x3 - 3 x2 + 5 x - 3 by x2 - 2

Sapling Academy · Accepted Answer

To divide the given polynomial, we can write the function as:

$\frac{	imes ^ 3 - 3 	imes ^ 2 + 5 	imes - 3}{	imes ^ 2 - 2}$

= $\frac{	imes ^ 3 + 5 	imes - 3 	imes ^ 2 - 3}{	imes ^ 2- 2}$

= $\frac{	imes ^ 3 - 2 	imes + 2 	imes + 5 	imes - 3 	imes ^ 2 - 3}{	imes ^ 2 - 2}$

= $\frac{(	imes ^ 3 - 2 	imes) + 7 	imes - 3 	imes ^ 2 - 3}{	imes ^ 2 - 2}$

= $\frac{	imes (	imes ^ 2 - 2) + 7 	imes - 3 	imes ^ 2 - 3}{	imes ^ 2 - 2}$

= $\frac{	imes (	imes ^ 2 - 2)}{	imes ^ 2 - 2} + \frac{ 7 	imes - 3 	imes ^ 2 - 3}{	imes ^ 2 - 2}$

= $ 	imes + \frac{ 7 	imes - 3 	imes ^ 2 - 3}{	imes ^ 2 - 2}$

= $ 	imes + \frac{ - 3 	imes ^ 2 - 3 + 7 	imes}{	imes ^ 2 - 2}$

= $ 	imes + \frac{ - 3 	imes ^ 2 + 6 - 6 - 3 + 7 	imes}{	imes ^ 2 - 2}$

= $ 	imes + \frac{ (- 3 	imes ^ 2 + 6) - 9 + 7 	imes}{	imes ^ 2 - 2}$

= $ 	imes + \frac{ - 3 ( 	imes ^ 2 - 2) - 9 + 7 	imes}{	imes ^ 2 - 2}$

= $ 	imes + \frac{ - 3 ( 	imes ^ 2 - 2)}{	imes ^ 2 - 2} + \frac {- 9 + 7 	imes}{	imes ^ 2 - 2}$

= $ 	imes - 3 + \frac {7 	imes - 9 }{	imes ^ 2 - 2}$

Therefore, When we divide X3 - 3 X2 + 5 X - 3 by X2 - 2, quotient is X - 3 and remainder is 7 X - 9.

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