Cho hai đa thức:
\(Q\left(x\right)=-x^5+2x^4-x^3+2x^2+x+1\)
\(P\left(x\right)=2x^5+x^4+2x^3-2x+2\)
Biết R(x) là đa thức thỏa mãn: \(Q\left(x\right)+R\left(x\right)=P\left(x\right)\). Hỏi \(R\left(x\right)=?\)
\(Q\left(x\right)+R\left(x\right)=P\left(x\right)\)\(\Leftrightarrow R\left(x\right)=P\left(x\right)-Q\left(x\right)\)
\(\Leftrightarrow R\left(x\right)=2x^5+x^4+2x^3-2x+2-\)\(\left(-x^5+2x^4-x^3+2x^2+x+1\right)\)
\(\Leftrightarrow R\left(x\right)=\left(2x^5+x^5\right)+\left(x^4-2x^4\right)+\left(2x^3+x^3\right)-2x^2+\left(-2x-x\right)+\left(2-1\right)\)
\(\Leftrightarrow R\left(x\right)=3x^5-x^4+3x^3-2x^2-3x+1\)
