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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. - 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.

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