Question

please help me this question is a not solve from me class 9th chapter name polynomial ​

Answer 1

Solution :

The given polynomial : x³ + 3x² + 3x + 1

To find : Remainders

Applied theorem : Remainder theorem ,

a ) x + π

The value of x would be x + π = 0

Then x = - π

$\sf{p(-\pi)\:=\:(-\pi)^3\:+\:3(-\pi)^2\:+\:3(-\pi)\:+\:1}$

Remainder = $\sf{-\pi^3\:-\:3\pi^2\:-\:3\pi\:+\:1}$

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b ) 5 + 2x

If 5 + 2x = 0

Then , 2x = -5

x = -5/2

$\sf{p(\dfrac{-5}{2})\:=\:(\dfrac{-5}{2})^3\:+\:3(\dfrac{-5}{2})^2\:+\:3(\dfrac{-5}{2})\:+\:1}$

$\sf{\implies\:\dfrac{-125}{8}\:+\:\dfrac{75}{4}\:-\:\dfrac{15}{2}\:+\:1}$

$\sf{\implies\:\dfrac{-125\:+\:150\:-\:60\:+\:8}{8}}$

Remainder : $\sf{\implies\:\dfrac{-35\:+\:8}{8}}$

$\sf{\implies\:\dfrac{-27}{8}}$

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