Cho các đa thức:
\(f\left(x\right)=5x^4+3x^2+x-1\); \(h\left(x\right)=-x^4+3x^3-2x^2-x+2\); \(g\left(x\right)=2x^4-x^3+x^2+2x+1\)
Hỏi đa thức \(f\left(x\right)+h\left(x\right)-g\left(x\right)=?\)
\(2x^4+4x^3-2x\). \(2x^4+x^3-x^2-2x+3\). \(3x^4+x^3-2x\). \(x^4+4x^3+2x\). Hướng dẫn giải:\(f\left(x\right)+h\left(x\right)-g\left(x\right)\)
\(=\)\(\left(5x^4+3x^2+x-1\right)+\)\(\left(-x^4+3x^3-2x^2-x+2\right)\) \(-\left(2x^4-x^3+x^2+2x+1\right)\)
\(=\left(5x^4-x^4-2x^4\right)+\left(3x^3+x^3\right)+\left(3x^2-2x^2-x^2\right)\)\(+\left(x-x-2x\right)+\left(-1+2-1\right)\)
\(=2x^4+4x^3-2x\)
