2. Polynomials
hard

બહુપદી $x^{3}+3 x^{2}+3 x+1$ નો $5+2 x$ ભાજક વડે ભાગાકાર કરો અને શેષ શોધો.

A

$\frac{8}{27}$

B

$-\frac{27}{8}$

C

$27$

D

$\frac{27}{8}$

Solution

$5+2 x$ નું શૂન્ય $\left(-\frac{5}{2}\right)$ છે.

$\left[\because 5+2 x=0, \,\,\therefore 5=-2 x,-\frac{5}{2}=x\right]$

$p(x)=x^{3}+3 x^{2}+3 x+1$ માં $x=-\frac{5}{2}$ મૂકી એ તો 

$p\left(-\frac{5}{2}\right) =\left(-\frac{5}{2}\right)^{3}+3\left(-\frac{5}{2}\right)^{2}+3\left(-\frac{5}{2}\right)+1$

$=-\frac{125}{8}+3\left(\frac{25}{4}\right)+\left(-\frac{15}{2}\right)+1$

$=-\frac{125}{8}+\frac{75}{4}-\frac{15}{2}+\frac{1}{1}$

$=\frac{-125+150-60+8}{8}$

$=\frac{-185+158}{8}=-\frac{27}{8}$

આમ, $x^{3}+3 x^{2}+x+1$ ની શેષ $-\frac{27}{8}$ મળે છે.

Standard 9
Mathematics

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