a) \(C\left(x\right)=5-8x^4+2x^3+x+5x^4+x^2-4x^3\)
\(=\left(-8x^4+5x^4\right)+\left(2x^3-4x^3\right)+x^2+x+5\)
\(=-3x^4-2x^3+x^2+x+5\)
\(D\left(x\right)=\left(3x^5+x^4-4x\right)-\left(4x^3-7+2x^4+3x^5\right)\)
\(=3x^5+x^4-4x-4x^3+7-2x^4-3x^5\)
\(=\left(3x^5-3x^5\right)+\left(x^4-2x^4\right)-4x^3-4x+7\)
\(=-x^4-4x^3-4x+7\)
b) \(P\left(x\right)=C\left(x\right)+D\left(x\right)\)
\(=\left(-3x^4-2x^3+x^2+x+5\right)+\left(-x^4-4x^3-4x+7\right)\)
\(=-3x^4-2x^3+x^2+x+5-x^4-4x^3-4x+7\)
\(=\left(-3x^4-x^4\right)+\left(-2x^3-4x^3\right)+x^2+\left(x-4x\right)+\left(5+7\right)\)
\(=-4x^4-6x^3+x^2-3x+12\)
\(Q\left(x\right)=C\left(x\right)-D\left(x\right)\)
\(=\left(-3x^4-2x^3+x^2+x+5\right)-\left(-x^4-4x^3-4x+7\right)\)
\(=-3x^4-2x^3+x^2+x+5+x^4+4x^3+4x-7\)
\(=\left(-3x^4+x^4\right)+\left(-2x^3+4x^3\right)+x^2+\left(x+4x\right)+\left(5-7\right)\)
\(=-2x^4+2x^3+x^2+5x-2\)
a: C(x)=-3x^4-2x^3+x^2+x+5
D(x)=-x^4-4x^3-4x+7
b: P(x)=-3x^4-2x^3+x^2+x+5-x^4-4x^3-4x+7
=-4x^4-6x^3+x^2-3x+12
Q(x)=-3x^4-2x^3+x^2+x+5+x^4+4x^3+4x-7
=-2x^4+2x^3+x^2+5x-2
