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What Number Should Be Added to 3x3 – 5x2 + 6x So that When Resulting Polynomial is Divided by X – 3, the Remainder is 8? - ICSE Class 10 - Mathematics

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Question

What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8? 

Solution

Let the numbw-er k be added and resulting polnomic be f(x). 

So, f(x) =`3x^3+5x^2+6x+k`  

it is given that when f(x)is dividing by (x-3), the remainder is 8. 

∴ f(3)=8 

`3(3)^3-5(3)^2+6(3)+k=8` 

`81-45+18+k=8` 

`54+k=8`

`k=-46` 

Thus, the required number is  -46. 

  Is there an error in this question or solution?

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Solution What Number Should Be Added to 3x3 – 5x2 + 6x So that When Resulting Polynomial is Divided by X – 3, the Remainder is 8? Concept: Remainder Theorem.
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