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