Find the number which should be added to $x^{2} + 6 x + 5$ so that the resulting polynomial is completely divisible by $x + 3$ .

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Solution

The correct option is B 4
Let K be added to make the given polynomial divisible by $(x + 3)$ . The new polynomial is:
$f (x) = x^{2} + 6 x + 5 + K$

Using factor theorem,
$f (- 3) = 0$
$(- 3)^{2} + 6 (- 3) + 5 + K = 0$
$9 - 18 + 5 + K = 0$
$K = 4$

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