Ex.2.3 Q3 Polynomials Solution - NCERT Maths Class 9

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Check whether \(7 + 3x\) is a factor of \(\begin{align}p(x)=3 x^{3}+7 x\end{align}\) .

 Video Solution
Ex 2.3 | Question 3

Text Solution


When a polynomial \(p (x)\) is divided by \(x-a\) and by the remainder theorem if \(p(a) = 0\) then \(x – a\) is a factor of \(p(x).\)


Let \(\begin{align}p(x)=3 x^{3}+7 x\end{align}\)

The root of \(\begin{align}7+3 x=0 \text { is } \frac{-7}{3}\end{align}\)

\[\begin{align} p\left(\frac{-7}{3}\right) &=3\left(\frac{-7}{3}\right)^{3}+7\left(\frac{-7}{3}\right) \\ &=\frac{3 \times(-343)}{27}+\frac{-49}{3} \\ &=\frac{-343-147}{9} \\ &=\frac{-490}{9} \neq 0 \end{align}\]

Since the remainder of \(\begin{align}p\left(\frac{-7}{3}\right) \neq 0,7+3 x\end{align}\) is not a factor of  \(\begin{align}3 x^{3}+7 x\end{align}\)

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