Question

When the polynomial x3+5x2+px+q is divided by (x+1) it leaves remainder 8, and when divided by (x-1) it leaves remainder 4. Find p and q ​

Answer 1

Answer:

p = -3
q = -13

Step-by-step explanation:

By remainder theorem,
f(x) = x^3 + 5x^2 + px + q
x-a = x+1
i) a= -1
f(-1) is remainder.
f(-1) = -1 + 25 - p + q
8 = 24-p+q
q-p=-16

ii) a=+1
f(+1)= 1 + 25 + p + q
4 = 26 + p + q
p+q = -22

-p + q = -16
p + q = -22
Subtracting equations,
-2p = 6
p = -3
q = =13