help solve 4

May 2010
39
0
let p(x)=(x+1)(x-3) Q(x)+a(x+1)+b where Q(X) is a polynomial and a and b are real numbers when p(x) is divided by (x+1) the remainder is -11
when p(x) is divided by (x-3) the remainder is 1
i)what it the value of b
ii)what is the remainder when p(x) is divided by (x+1)(x-3)

with working out please
 
Oct 2009
4,261
1,836
let p(x)=(x+1)(x-3) Q(x)+a(x+1)+b where Q(X) is a polynomial and a and b are real numbers when p(x) is divided by (x+1) the remainder is -11


And this means that \(\displaystyle p(-1)=-11\)


when p(x) is divided by (x-3) the remainder is 1


And this means \(\displaystyle p(3)=1\) . Now just substitute and evaluate directly the values you want. (Nod)

Tonio

i)what it the value of b
ii)what is the remainder when p(x) is divided by (x+1)(x-3)

with working out please
.