If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor $= x - 1$ and remainder $= 2$ , then the quotient will be .

x^{3} + x^{2} + 1

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x^{3} + 2 x^{2} + 1

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x^{3} + 2 x^{2} + x + 1

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Solution

The correct option is B $x^{3} + 2 x^{2} + 1$
$D i v i d e n d = Q u o t i e n t \times D i v i s o r + R e m a i n d e r$
Let Quotient be q(x).

So, $x^{4} + x^{3} - 2 x^{2} + x + 1 = (x - 1) q (x) + 2$

$⟹ x^{4} + x^{3} - 2 x^{2} + x - 1 = (x - 1) q (x)$

$\begin{matrix} x^{3} + 2 x^{2} + 1 x - 1 x^{4} + x^{3} - 2 x^{2} + x - 1 - x^{4} + x^{3} - -------- - 2 x^{3} - 2 x^{2} + x - 1 - 2 x^{3} + 2 x^{2} - ----------- - x - 1 - x + 1 - ------ - 0 \end{matrix}$

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If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor = $x - 1$ and remainder = 2. Find the quotient q(x)

$If the dividend = x^{4} + x^{3} - 2 x^{2} + x + 1, divisor = x - 1 and remainder = 2, then find the quotient q(x) .$

x^{4} + x^{3} - 2 x^{2} + x + 1

x - 1

2

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ and divisor = $(x - 1)$ , find the quotient, $q (x)$ and remainder $r (x)$ .

When x^{4} + x^{3} - 2 x^{2} + x + 1 is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

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