Question

if polynomial p(x) is a factor of polynomials q(r),then q(r) is _____ of p(x)​

Answer 1

Step-by-step explanation:

Let p(x) and g(x) be two polynomials

If g(x) is any polynomial then it can divide p(x) by q(x) where 0<q(x) and may get a remainder say r(x).

If g(x) perfectly divides p(x) by q(x), then r(x)=0.

It is obvious that deg r(x)<deg g(x).

∴ we can find polynomial q(x) and r(x) such that

p(x)=q(x)q(x)+r(x), where r(x)=0 or deg r(x)<deg g(x)

Answer 2

Let p(x) and g(x) be two polynomials

If g(x) is any polynomial then it can divide p(x) by q(x) where 0<q(x) and may get a remainder say r(x).

If g(x) perfectly divides p(x) by q(x), then r(x)=0.

It is obvious that deg r(x)<deg g(x).

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∴ we can find polynomial q(x) and r(x) such that

p(x)=q(x)q(x)+r(x), where r(x)=0 or deg r(x)<deg g(x)