Divide the polynomial x³ - 3x² + 5x - 3 by x²

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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