Subtract the second polynomial from the first :

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

2 x^{2} + x - 2

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

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

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x + 2 x^{2} - 2

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Solution

The correct option is A $x^{3} + 2 x^{2} + x - 2$
$\begin{matrix} (x^{4} + x^{2} + x - 1) - (x^{4} - x^{3} - x^{2} + 1) & = x^{4} + x^{2} + x - 1 - x^{4} + x^{3} + x^{2} - 1 = x^{4} - x^{4} + x^{3} + x^{2} + x^{2} + x - 1 - 1 = x^{3} + 2 x^{2} + x - 2 \end{matrix}$

Hence, option $B$ is correct.

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Similar questions

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

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

x - 1

2

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