a/ \(P\left(x\right)=x^5-3x^2+7x^4-9x^3+x^2-\dfrac{1}{4}x\)
\(=x^5+7x^4-9x^3+\left(x^2-3x^2\right)-\dfrac{1}{4}x\)
\(=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x\)
\(Q\left(x\right)=5x^4-x^5+x^2-2x^3+3x^2-\dfrac{1}{4}\)
\(=-x^5+5x^4-2x^3+\left(x^3+3x^2\right)-\dfrac{1}{4}\)
\(=-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}\)
b/ \(P\left(x\right)+Q\left(x\right)=x^5+7x^4-9x^3-2x^2-\dfrac{1}{4}x-x^5+5x^4-2x^3+4x^2-\dfrac{1}{4}\)
\(=\left(x^5-x^5\right)+\left(7x^4+5x^4\right)-\left(9x^3+2x^3\right)+\left(4x^2-2x^2\right)-\dfrac{1}{4}x-\dfrac{1}{4}\)
\(=12x^4-11x^3+2x^2-\dfrac{1}{4}x-\dfrac{1}{4}\)