Bài 1
a) \(A\left(x\right)=-x^4+7x^2+2x^3-10+6x^4-3x^3+5x-x^2\)
\(=\left(-x^4+6x^4\right)+\left(2x^3-3x^3\right)+\left(7x^2-x^2\right)+5x-10\)
\(=5x^4-x^3+6x^2+5x-10\)
\(B\left(x\right)=2x^4+6-x^3+7x-5x^2+4x^3-x^4+2x^2\)
\(=\left(2x^4-x^4\right)+\left(-x^3+4x^3\right)+\left(-5x^2+2x^2\right)+7x+6\)
\(=x^4+3x^3-3x^2+7x+6\)
\(C\left(x\right)=3x^4+3x-4x^4+5x^3-x^2+4x-7-8x^3\)
\(=\left(3x^4-4x^4\right)+\left(5x^3-8x^3\right)-x^2+\left(3x+4x\right)-7\)
\(=-x^4-3x^3-x^2+7x-7\)
b) \(A\left(x\right)+B\left(x\right)+C\left(x\right)=\left(5x^4-x^3+6x^2+5x-10\right)+\left(x^4+3x^3-3x^2+7x+6\right)+\left(-x^4-3x^3-x^2+7x-7\right)\)
\(=5x^4-x^3+6x^2+5x-10+x^4+3x^3-3x^2+7x+6-x^4-3x^3-x^2+7x-7\)
\(=\left(5x^4+x^4-x^4\right)+\left(-x^3+3x^3-3x^3\right)+\left(6x^2-3x^2-x^2\right)+\left(5x+7x+7x\right)+\left(-10+6-7\right)\)
\(=5x^4-x^3+2x^2+19x-11\)
\(A\left(x\right)-B\left(x\right)-C\left(x\right)=\left(5x^4-x^3+6x^2+5x-10\right)-\left(x^4+3x^3-3x^2+7x+6\right)-\left(-x^4-3x^3-x^2+7x-7\right)\)
\(=5x^4-x^3+6x^2+5x-10-x^4-3x^3+3x^2-7x-6+x^4+3x^3+x^2-7x+7\)
\(=\left(5x^4-x^4+x^4\right)+\left(-x^3-3x^3+3x^3\right)+\left(6x^2+3x^2+x^2\right)+\left(5x-7x-7x\right)+\left(-10-6+7\right)\)
\(=5x^4-x^3+10x^2-9x-9\)
