$x^{3} - x - 4$ added to $x^{4} - x^{3} - x^{2} + x + 3$ to obtain $x^{4} + x^{2} - 1$ ?
If true then enter $1$ and if false then enter $0$

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Solution

Let the expression to be added be $A$
Given, $(x^{4} - x^{3} - x^{2} + x + 3) + A = x^{4} + x^{2} - 1$
$=> A = (x^{4} + x^{2} - 1) - (x^{4} - x^{3} - x^{2} + x + 3)$
$A = x^{4} + x^{2} - 1 - x^{4} + x^{3} + x^{2} - x - 3 = x^{3} + 2 x^{2} - x - 4$

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x3−x−4 added to x4−x3−x2+x+3 to obtain x4+x2−1 ?If true then enter 1 and if false then enter 0

Let the expression to be added be A Given, (x4−x3−x2+x+3)+A=x4+x2−1=>A=(x4+x2−1)−(x4−x3−x2+x+3)A=x4+x2−1−x4+x3+x2−x−3=x3+2x2−x−4

$x^{3} - x - 4$ added to $x^{4} - x^{3} - x^{2} + x + 3$ to obtain $x^{4} + x^{2} - 1$ ?
If true then enter $1$ and if false then enter $0$

Let the expression to be added be $A$
Given, $(x^{4} - x^{3} - x^{2} + x + 3) + A = x^{4} + x^{2} - 1$
$=> A = (x^{4} + x^{2} - 1) - (x^{4} - x^{3} - x^{2} + x + 3)$
$A = x^{4} + x^{2} - 1 - x^{4} + x^{3} + x^{2} - x - 3 = x^{3} + 2 x^{2} - x - 4$