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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. - ICSE Class 10 - 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 `

  Is there an error in this question or solution?
Solution 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. Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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