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Theorems for Continuity

Find the valu...

Question

Find the value of the reminder obtained when $6 x^{4} + 5 x^{3} - 2 x + 8$ is divided by $x - \frac{1}{2}$ .

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Solution

The correct option is D $8$
$6 x^{4} + 5 x^{3} - 2 x + 8$
$= 6 x^{3} (x - \frac{1}{2}) + 8 x^{3} - 2 x + 8$
$= 6 x^{3} (x - \frac{1}{2}) + 2 x (4 x^{2} - 1) + 8$
$= 6 x^{3} (x - \frac{1}{2}) + 2 x (2 x - 1) (2 x + 1) + 8$
$= 6 x^{3} (x - \frac{1}{2}) + 4 x (x - \frac{1}{2}) (2 x + 1) + 8$ .
Hence the remainder will be $8$ .

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