If (x+a) is a factor of two polynomials x2+px+q and x2+mx+n, then prove that :

a=n- q/m-pp(x)= x^{2}+px+q

g(x)= x+a

x = -a

p(-a)= a^{2}-ap+q=0 1st equatioon

p_{1}(x)=x^{2}+mx+n

p_{1}(-a)=a^{2}-am+n=0 2nd equation

on equating 1 and 2

a^{2}-am+n=a^{2}-ap+q

-am+ap=q-n

-a(m-p)=q-n

-a= q-n/m-p

a= n-q/m-p

hence proved