#### Question

What number should be added to 3x^{3} – 5x^{2} + 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?

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.