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Purely Imaginary

What must be ...

Question

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

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Solution

Let $p (x)$ be subtracted

Then $2 x^{4} + 4 x^{2} - 3 x + 7 - p (x) = 3 x^{3} - x^{2} + 2 x + 1$

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

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