Question

Answer 1

a) \(P\left(x\right)=3x^4+\left(8x^3-2x^3\right)+\left(7x^2-6x^2\right)-4x+2-4\)
\(=3x^4+6x^3+x^2-4x-2\)
\(Q\left(x\right)=\sqrt{2x^4}-\sqrt{2x^4}+\dfrac{7}{2}x^3-\dfrac{1}{2}x^3+\dfrac{7}{2}x^2-\dfrac{1}{2}x^2+2x+7\)
\(=3x^3+3x^2+2x+7\)
b) \(P\left(x\right)+Q\left(x\right)=3x^4+6x^3+x^2-4x-2+3x^3+3x^2+2x+7\)
\(=3x^4+9x^3+4x^2-2x+5\)
\(P\left(x\right)-Q\left(x\right)=3x^4+6x^3+x^2-4x-2-\left(3x^3+3x^2+2x+7\right)\)
\(=3x^4+3x^3-2x^2-6x-9\)