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What Number Should Be Subtracted from X3 + 3x2 – 8x + 14 So that on Dividing It with X – 2, the Remainder is 10. - ICSE Class 10 - Mathematics

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Question

What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it with x – 2, the remainder is 10. 

Solution

Let the number to be subtracted be k and the resulting polynomial be f(x). 

So, f(x)=`x^3+3x^2-8x+14-k` 

it is given that when f(x) is divided by (x-2), the remainder is 10. 

`f(2)=10`   

`(2)^3+3(2)^2-8(2)+14-k=10` 

`8+12-16+14-k=10` 

 18-k=10  

k=8 

Thus, the requied number is 8.

 

  Is there an error in this question or solution?

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Solution What Number Should Be Subtracted from X3 + 3x2 – 8x + 14 So that on Dividing It with X – 2, the Remainder is 10. Concept: Remainder Theorem.
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