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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