Question

If f(x) is divided byx−3 then the remainder is 5 , and when it is divided by (x−4) the remainder is '0' . Then the remainder when it is divided by (x−3)(x−4) is​

Answer 1

Step-by-step explanation:

Let us consider the polynomial function as f(x).

Now as per first equation, f(x)=g(x)*(x-3) + 5 and f(x)=h(x)*(x-4) + 7. (say)

Now, f(x)/(x-3)(x-4) can be grouped into f(x)/(x-4) - f(x)/(x-3). (Equation 1)

Now we have, f(x)/(x-3) = g(x) + 5/(x-3) and f(x)/(x-4) = h(x) + 7/(x-4).

Now substituting in Equation 1, we have f(x)/(x-3)(x-4) = h(x) - g(x) + (7/(x-4) - 5/(x-3), which comes out to be h(x) - g(x) + (2x - 1)/((x-4)*(x-3)).

Therefore, from her we can comment that the remainder is (2x - 1).

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