What must be subtracted from $x^{4} + 2 x^{2} - 3 x + 7$ to get $x^{3} + x^{2} + x - 1$ ?

x^{4} - x^{3} + x^{2} - 4 x + 8

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x^{3} + x^{2} - 4 x + 8

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x^{4} - x^{3} + x^{2} + 4 x - 8

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x^{4} - x^{3} - x^{2} + 4 x - 8

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Solution

The correct option is A $x^{4} - x^{3} + x^{2} - 4 x + 8$
Let the polynomial to be subtracted be a

$\Rightarrow (x^{4} + 2 x^{2} - 3 x + 7) - a = (x^{3} + x^{2} + x - 1)$
$\Rightarrow a = (x^{4} + 2 x^{2} - 3 x + 7) - (x^{3} + x^{2} + x - 1)$
$= x^{4} - x^{3} + (2 - 1) x^{2} - (3 + 1) x + (7 + 1)$
$= x^{4} - x^{3} + x^{2} - 4 x + 8$
$∴$ Polynomial to be subtracted is $x^{4} - x^{3} + x^{2} - 4 x + 8$

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