If the polynomial $x^{3} - a x^{2} + 2 x - a$ is divided $x - a,$ then remainder is:

a^{3}

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a^{2}

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a

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- a

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Solution

The correct option is C $a$
According to remainder theorem, when $f (x)$ is divided by $(x - a)$ , then the remainder is equal to $f (a)$ .

So,
$\begin{matrix} f (x) & = x^{3} - a x^{2} + 2 x - a f (a) & = (a)^{3} - a (a)^{2} + 2 (a) - a = a^{3} - a^{3} + 2 a - a = a \end{matrix}$

So, option $C$ is the correct answer.

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If the polynomial x3−ax2+2x−a is divided x−a, then remainder is:

The correct option is C aAccording to remainder theorem, when f(x) is divided by (x−a), then the remainder is equal to f(a).So, f(x)=x3−ax2+2x−af(a)=(a)3−a(a)2+2(a)−a=a3−a3+2a−a=aSo, option C is the correct answer.

If the polynomial $x^{3} - a x^{2} + 2 x - a$ is divided $x - a,$ then remainder is: