Question

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$what \: \: must \: \: be \: \: added \: \: to \: \: x {}^{2} + 4x - 6 \: \: \: \: \: \:to \: \: get \: \: \: \: \: x {}^{4} - x {}^{3} + 2x {}^{2} - 5$
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Answer 1

$Let \: A= x^{2} + 4x- 6 \: and\: B = x^{4} - x^{3} + 2x^{2} - 5$

$Let \: P \: is \: added\: to \: A \: to \: get \: B$

$\implies A + P = B$

$\implies P = B - A$

$= x^{4} - x^{3} + 2x^{2} - 5 - ( x^{2} + 4x- 6)\\= x^{4} - x^{3} + 2x^{2} - 5 - x^{2} - 4x+6\\= x^{4} - x^{3} +x^{2} -4x +1$

Therefore.,

$\red{Required \: expression \: should}\\\red{ be \: added }\green { = x^{4} - x^{3} +x^{2} -4x +1 }$

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Answer 2

Answer:

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