Question

When the polynomial f(x)=5x^4 + 4x^3 + 3x^2 + Px + Q is divided by x^2 - 1, the remainder is zero. Determine the value of P + Q

Answer 1

(x^2 - 1) ( a x^2 + b x + c) = 5x^4 + 4x^3 + 3 x^2 + Px + Q

x^2 ( a x^2 + b x + c) = ax^4 + b x^3 + c x^2
-1 ( a x^2 + b x + c) = 0x^4 + 0 x^3 - a x^2 - b x - c

add = a x^4 + b x^3 +(c-a) x^2 - b x - c

a = 5
b = 4
c - a = 3 so c = 8
P = -b = -4
Q = -c = -8

Answer 2

or, you can do a long division
or two synthetic divisions using +1 and -1