Factorization Of Polynomials — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Polynomials2 Marks
Question
Find the remainder when $x^3+3 x^3+3 x+1$ is divided by: $x-\frac{1}{2}$
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Answer
Here, $f(x) = x3 + 3x2 + 3x + 1$ By remainder theorem $\text{x}-\frac{1}{2}$
$\Rightarrow\ \text{x}=\frac{1}{2}$ substitute the value of x in f(x) $\text{f}\Big(\frac{1}{2}\Big)=\Big(\frac{1}{2}\Big)^3+3\Big(\frac{1}{2}\Big)^2+3\Big(\frac{1}{2}\Big)+1$
$=\Big(\frac{1}{2}\Big)^3+3\Big(\frac{1}{2}\Big)^2+3\Big(\frac{1}{2}\Big)+1$
$=\frac{1}{8}+\frac{3}{4}+\frac{3}{2}+1$
$=\frac{1+6+12+8}{8}$
$=\frac{27}{8}$
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