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$If P = 5 x^{4} - 2 x^{2} + 4 x - 3, Q = 5 x^{4} + 3 x^{3} - 4 x + 3, what is P - Q ?$

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$- 3 x^{3} - 2 x^{2} + 8 x - 6$

$3 x^{3} - 2 x^{2} + 8 x - 6$

$- 3 x^{3} + 2 x^{2} + 8 x - 6$

$x^{3} - 2 x^{2} + 8 x - 6$

answer is A.

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Detailed Solution

$P - Q = 5 x^{4} - 2 x^{2} + 4 x - 3 - (5 x^{4} + 3 x^{3} - 4 x + 3)$

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

$(change signs correctly!)$

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

$= - 3 x^{3} - 2 x^{2} + 8 x - 6$

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