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# Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3. - Mathematics

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#### Question

Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.

#### Solution

Let the number to be subtracted from the given polynomial be k

let f(y)=3y^3+y^2-22y+15-k

it is given that f(y) is divisible by (y+3)

Remainder=f(-3) =0

3(-3)^3+(-3)^2-22(-3) +15-k=0

-81+9+66+15-k=0

9-k=0

k=9

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