When a polynomial p(x) is divided by x+1 the remainder is 5. When p(x) is divided by x+5 the remainder is -7 Find the remainder when p(x) is divided by (x+1)(x+5).

p(-1)=5 p(-5)=-7

there is probably some super short cut now but I don't know it.

p(x)=Q(x)(x+1)(x+5)+Ax+B

So when divided by (x+1)(x+5) the remainder will be Ax+B

p(-1)=A(-1)+B=-A+B=5

p(-5)=A(-5)+B=-5A+B=-7

solve simultaneously

-A+B=5

-5A+B=-7