What must be subtracted from $(x^{3} + 5 x^{2} + 5 x + 8)$ so that the resulting polynomial is exactly divisible by $(x^{2} + 3 x - 2)$ ?

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Solution

It is given that the dividend is $p (x) = x^{3} + 5 x^{2} + 5 x + 8$ , the divisor is $g (x) = x^{2} + 3 x - 2$ , therefore, the division is as shown above.

Therefore, from the division, we get that the remainder is $x + 12$ .

Hence, $x + 12$ must be subtracted from $x^{3} + 5 x^{2} + 5 x + 8$ so that the resulting polynomial is exactly divisible by $x^{2} + 3 x - 2$ .

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Respected Sir,

Please help me in solving my below mentioned doubt:

What must be subtracted from x³- 6x² - 15x + 80 so that the resulting polynomial is exactly divisible by x²+ x + 22?

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