Question

x^3 + 8x^2 + px - 25 leaves a remainder of R when divided by (x-1) and a remainder of -R when divided by (x+2). Find the value of p.



I've solved it already, but i'm not suree whether i've done it right. Can anyone else solve it as well and tell me what answer they get??? I got p as -17.

Answer 1

you are correct.

Answer 2

thankuuuuuu :)

Answer 3

Let t(x)= x^3 + 8x^2 + px -25
and g(x)= x-1
Now, t(1)= 1^3 + 8 + p - 25= 1+8+p-25=p-16
Since, remainder is R, we get, p-16=R.....(i)
Next, it is divided by (x+2).
So, t(-2)= (-2)^3 + 8(-2)^2 -2p -25= -8+32-25-2p=-2p-1
Now, since remainder is -R,
we get -2p-1=-R........(ii)
Solving (i), (ii), we get,
p-16=2p+1
Or, p=-17