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What must be added to f(x) =4x^2 +2x^3-2x^2+x-1 so that the resulting polynomial is divisible by g(x)=x^2+2x-3

Posted by Kumkum Sethiya 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 7 months ago

Question: What must be added to f(x) = 4x⁴ + 2x³ – 2x²+ x – 1 so that the resulting polynomial is divisible by g(x) = x² + 2x – 3?

By division algorithm, we have

Clearly, RHS is divisible by g(x). Therefore, LHS is also divisible by g(x). Thus, if we add – r(x) to f(x) then the resulting polynomial is divisible by g(x). Let us now find the remainder when f(x) is divided by g(x).

Hence, we should add –r(x) = 61x – 65 to f(x) so that the resulting polynomial is divisible by g (x).

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