Question

What must be added to the polynomial f(x) so that the resulting polynomial is exactly divisible by g​

Answer 1

$\:$

we know that

f(x) = g(x) × q(x) + r(x)

f(x) - r(x) = g(x) × q(x)

f(x) + {-r(x)} = g(x) × q(x)

clearly right hand side is divisible by g(x)

therefore the left hand side is also divisible by g(x) does every add -r(x) to f(x) then the resulting polynomial is divisible by g(x)

let us now find the reminder when f(x) is divided by g(x)

(refer the following image for dividing method)

Answer :- hence we should add -r(x) = x - 2 to f(x) show the resulting polynomial is divisible by g(x)

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