Let - x -x-1 2x2-5 x3-1 2x2-5 2x-2 x3-3 x3-1 x-1 3x2-2 and ax-b be the remainder when - x is divided by x2-1- find 2a-b-

Δ( x ) = x 1 amp; 2x^ 2 5 amp; x^ 3 1 2x^ 2 +5 amp; 2x+2 amp; x^ 3 +3 x^ 3 1 amp; x+1 amp; 3x^ 2 2 and ax+b ...

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Definition of a Determinant

Let Δ x =x-...

Question

Let $Δ (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} x - 1 & 2 x^{2} - 5 & x^{3} - 1 2 x^{2} + 5 & 2 x + 2 & x^{3} + 3 x^{3} - 1 & x + 1 & 3 x^{2} - 2 \end{matrix} ∣ ∣ ∣ ∣ ∣$ and $a x + b$ be the remainder when $Δ (x)$ is divided by $x^{2} - 1$ , find $2 a + b$ .

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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).

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

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2

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

p (x)

g (x)

q (x)

r (x)

p (x)

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

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