What must be added to the polynomial $14 x^{2} + 13 x - 15$ so that the resulting polynomial is exactly divisible by $7 x - 4.$

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Solution

Let $p (x) = 14 x^{2} + 13 x - 15$ and $q (x) = 7 x - 4$
Divide $p (x)$ by $q (x)$ by long division method as shown in the above image.
Therefore, the remainder is $- 3$ .
Hence, $3$ must be added to $14 x^{2} + 13 x - 15$ so that the resulting polynomial is exactly divisible by $7 x - 4$ .

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