Question

If the polynomials f1and f2 are not divisible by the polynomial g , can their sum fit F1+F2 be
divisible by g? Explain in detail.​

Answer 1

Given :    polynomials f1and f2 are not divisible by the polynomial g

To Find :  can their sum   F1+F2 be divisible by g

Solution:

polynomials f1and f2 are not divisible by the polynomial g  

Yes  their sum   F1+F2 be divisible by g

Example :  f1  = x²   +  1 , f2  = x²   - 1  , g(x) = x  or x²

f1  = x²   +  1

Not divisible by x  / x²

f2  = x²   - 1

Not divisible by x   / x²

Added both f1 + f2  = 2x²

divisible by x   / x²

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