What must be subtracted form $4 x^{2}$ to get $6 x^{3} - 2 x^{2} + 5 x - 1$ .

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Solution

Let $f$ should be subtracted from $4 x^{2}$ to get $6 x^{3} - 2 x^{2} + 5 x - 1$ .

Therefore,

$4 x^{2} - f = 6 x^{3} - 2 x^{2} + 5 x - 1$

$\Rightarrow f = 4 x^{2} - 6 x^{3} + 2 x^{2} - 5 x + 1 = - 6 x^{3} + 6 x^{2} - 5 x + 1$

Hence $(- 6 x^{3} + 6 x^{2} - 5 x + 1)$ should be subtracted from $4 x^{2}$ to get $6 x^{3} - 2 x^{2} + 5 x - 1$ .

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