$- x^{3} - 4 x^{2} + 9 x - 3$ must be subtracted from $x^{3} - 3 x^{2} + 5 x - 1$ to get $2 x^{3} + x^{2} - 4 x + 2$ . State true or false.

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Solution

The correct option is A

Let us verify the statement by subtracting $- x^{3} - 4 x^{2} + 9 x - 3$ from $x^{3} - 3 x^{2} + 5 x - 1$ .

The statement holds true if the difference is $2 x^{3} + x^{2} - 4 x + 2$ .

Now, $(x^{3} - 3 x^{2} + 5 x - 1) - (- x^{3} - 4 x^{2} + 9 x - 3)$

$= x^{3} - 3 x^{2} + 5 x - 1 + x^{3} + 4 x^{2} - 9 x + 3$

$= 2 x^{3} + x^{2} - 4 x + 2$

Hence the given statement is true.

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