# Ex.2.3 Q3 Polynomials Solution - NCERT Maths Class 9

Go back to  'Ex.2.3'

## Question

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

Video Solution
Polynomials
Ex 2.3 | Question 3

## Text Solution

Reasoning:

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 $$p(x).$$

Steps:

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}

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school