• # question_answer What must be added to $({{x}^{3}}-3{{x}^{2}}+4x-15)$ to obtain a polynomial, which is exactly divisible by $(x-y)$? A)  3      B)  - 8    C)  14      D)  ? 4

Correct Answer: A

Solution :

Let $f(x)={{x}^{3}}-3{{x}^{2}}+4x-15$ Let m to be added, then $\therefore$ $g(x)\times f(x)+m$ $\Rightarrow$ $g(x)={{x}^{3}}-3{{x}^{2}}+4x-15+m$ $\Rightarrow$ $g(3)=0$ $\Rightarrow$       $g(3)={{(3)}^{3}}-3\times {{(3)}^{2}}+4(3)-15+m=0$ $\Rightarrow$ $m-3=0$ $\therefore$ $m=3$

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