Find what must be subtracted from the polynomial $4 y^{4} + 12 y^{3} + 6 y^{2} + 50 y + 26$ so that the obtained polynomial is exactly divisible by $y^{2} + 4 y + 2$ .

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Solution

Polynomial is $4 y^{4} + 12 y^{3} + 6 y^{2} + 50 y + 26$
Divisor $= y^{2} + 4 y + 2$
Divisor -

So, remainder $= 2 y - 2$
so $2 y - 2$ must be subtracted from the polynomial so that the obtained polynomial is exactly divisible by $y^{2} + 4 y + 2.$
Hence, the answer is $2 y - 2.$

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