Question

If p(x) and g(x) are two polynomials with g(x)≠0, then we can find polynomial q(x) and r(x) such that p(x)= g(x)xq(x) + r(x), where r(x)=0 or degree of r(x)< degree of g(x). If p(x)= x2+ 2x+ 1 and g(x)= x+1, then i) Value of q(x) is? ii) Value of r(x) is? iii) Write degree of q(x). iv) Write degree of r(x). v) Verify p(x)= g(x)xq(x) + r(x).​

Answer 1

Answer:

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)

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)