# Ex.2.3 Q2 Polynomials Solution - NCERT Maths Class 9

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## Question

Find the remainder when \begin{align}x^{3}-a x^{2}+6 x-a\end{align} is divided by $$x - a.$$

Video Solution
Polynomials
Ex 2.3 | Question 2

## Text Solution

Reasoning:

Let $$p(x)$$ be any polynomial of degree greater than or equal to one and let $$a$$ be any real number. If a polynomial $$p(x)$$ is divided by \begin{align}x-a\end{align} then the remainder is $$p(a).$$

Steps:

Let \begin{align}p(x)=x^{3}-a x^{2}+6 x-a\end{align}

The root of $$x-a = 0$$ is $$a.$$

\begin{align} p(a) &=(a)^{3}-a(a)^{2}+6(a)-a \\ &=a^{3}-a^{3}+5 a \\ &=5 a \end{align}

Hence by remainder theorem, \begin{align}5 a\end{align} is the remainder when \begin{align}x^{3}-a x^{2}+6 x-a\end{align}  is divided by $$x - a.$$

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