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

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Solution

$Given: Dividend = x^{4} + x^{3} - 2 x^{2} + x + 1,$ $divisor = x - 1 and remainder = 2$
$To find: Quotient q (x)$

$\begin{matrix} x^{3} + 2 x^{2} + 1 x - 1 x^{4} + x^{3} - 2 x^{2} + x - 1 - x^{4} + x^{3} - ----------------- - 2 x^{3} - 2 x^{2} + x - 1 - 2 x^{3} + 2 x^{2} - --------------------- - 0 x^{2} + x - 1 - x + 1 - ---------- - 0 \end{matrix}$ $Hence, the quotient is x^{3} + 2 x^{2} + 1.$

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(x+1) is a factor of the polynomial
(a) $x^{3} + x^{2} - x + 1$
(b) $x^{3} + 2 x^{2} - x - 2$
(c) $x^{3} + 2 x^{2} - x + 2$
(d) $x^{4} + x^{3} + x^{2} + 1$

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

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

Q. If dividend =

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

, divisor

= x - 1

and remainder

= 2

, then the quotient will be .

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

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If the dividend = x4+x3−2x2+x+1,divisor = x−1 and remainder = 2,then find the quotient q(x).

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