8a. \(A\left(x\right)=3x^5+2x^4-4x^3+x^2-2x+1\) đã được thu gọn.
\(B\left(x\right)=-x^4+3x^3-2x^2+x^3-3x+2-3x^4\)
\(=-4x^4+4x^3-2x^2-3x+2\)
8b. \(A\left(x\right)+B\left(x\right)=3x^5+2x^4-4x^3+x^2-2x+1+\left(-4x^4+4x^3-2x^2-3x+2\right)\)
\(=3x^5+2x^4-4x^3+x^2-2x+1-4x^4+4x^3-2x^2-3x+2\)
\(=3x^5-2x^4-x^2-5x+3\)
\(A\left(x\right)-B\left(x\right)=3x^5+2x^4-4x^3+x^2-2x+1-\left(-4x^4+4x^3-2x^2-3x+2\right)\)
\(=3x^5+2x^4-4x^3+x^2-2x+1+4x^4-4x^3+2x^2+3x-2\)
\(=3x^5+6x^4-8x^3+3x^2+x-1\)
9. \(h\left(x\right)=g\left(x\right)-f\left(x\right)\)
9a. \(h\left(x\right)=x+3-\left(x^2+2x-1\right)\)
\(=x+3-x^2-2x+1\)
\(=-x^2-x+4\)
9b. \(h\left(x\right)=-5x^4+3x^3-2x^2-5x+3-\left(x^4-3x^3+2x-1\right)\)
\(=-5x^4+3x^3-2x^2-5x+3-x^4+3x^3-2x+1\)
\(=-6x^4+6x^3-2x^2-7x+4\)
