What must be subtracted from $8 x^{4} + 14 x^{2} + 7 x - 10$ So that the difference is exactly divisible by $4 x^{2} + 3 x - 2$ ?

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Solution

Let the given expression is subtracted from $A$
$\frac{A - 8 x^{4} - 14 x^{2} - 7 x + 10}{4 x^{2} + 3 x - 2} = 1$
$A - 8 x^{4} - 14 x^{2} - 7 x + 10 = 4 x^{2} + 3 x - 2$

$A = 4 x^{2} + 3 x - 2 + 8 x^{4} + 14 x^{2} + 7 x - 10$

$A = 8 x^{4} + 18 x^{2} + 10 x - 12$

Hence, this is the required expression.

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