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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
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Answer

Let p(x) = x3 + 3x2 + 3x + 1
5 + 2x = 0
$\Rightarrow$ 2x = -5
$\Rightarrow$ x =  -$\frac{5}{2}$
 = (-$\frac{5}{2}$)3 + 3(-$\frac{5}{2}$)2 + 3(-$\frac{5}{2}$) + 1
 = -$\frac{125}{8}$ + $\frac{75}{4}$ - $\frac{15}{2}$ + 1 = -$\frac{27}{8}$ 

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