a) P(x)=4x^3 + 2x^2 - 2x + 7 - x^2 - x
=>P(x)=4x^3 + 2x^2 - x^2 - 2x + 7 - x
=>P(x)=4x^3 + x^2 - 3x + 7
Q(x)= -4x^3 + x - 14 - 2x - x^2 - 1
=>Q(x)= -4x^3 - x^2 + x - 2x - 14 - 1
=>Q(x)= -4x^3 - x^2 - x - 15
b) P(x) + Q(x) = (4x^3 + x^2 - 3x + 7) + (-4x^3 - x^2 - x - 15)
P(x) + Q(x) = 4x^3 + x^2 - 3x + 7 + -4x^3 - x^2 - x - 15
P(x) + Q(x) = 4x^3 -4x^3 + x^2 - x^2 - 3x - x + 7 - 15
P(x) + Q(x) = -4x -8
P(x) - Q(x) = (4x^3 + x^2 - 3x + 7) - (-4x^3 - x^2 - x - 15)
P(x) - Q(x) = 4x^3 + x^2 - 3x + 7 + 4x^3 + x^2 + x + 15
P(x) - Q(x) = 8x^3 + 2x^2 - 2x +22
c) P(x)=4x^3 + x^2 - 3x + 7
Q(x)= -4x^3 - x^2 - x - 15
P(x)=-Q(x)
=> 4x^3 + x^2 - 3x + 7 = -(-4x^3 - x^2 - x - 15)
=> 4x^3 + x^2 - 3x + 7 = 4x^3 + x^2 + x + 15
=> x=-2