Question

If x ^4 + 3 X square + 7 is divided by 3 X + 5 then the possible degrees of the quotient and remainder are

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Given :

x⁴ + 3x² + 7x is devided by 3x + 5.

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☯ To Find :

We have to find the quotient and remainder.

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☯ Explanation :

$\sf{→ 3x + 5 = 0} \\ \\ \sf{→ 3x = -5} \\ \\ \sf{→ x = \frac{-5}{3}}$

Put Value of x in polynomial

$\sf{→ \bigg(\frac{-5}{3}\bigg)^4 + \bigg(\frac{-5}{3}\bigg)^2 + 7} \\ \\ \sf{→ \frac{625}{81} + \frac{25}{9} + 7} \\ \\ \bf{Taking \: LCM} \\ \\ \sf{→ \frac{625 + 225 + 567}{81}} \\ \\ \sf{→ \frac{1417}{81}}$

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★ Also refer to the Attachment.

➡ Remainder = $\sf{\frac{599}{81}}$

➡ Quotient = $\sf{ \frac{x^3}{3} - \frac{5x^2}{8} + \frac{32}{27} - \frac{32}{81}}$

Answer 2

Answer:

3,0

Step-by-step explanation: