a) Thu gọn đa thức P:
\(P\left(x\right)=2x^3-3x+x^5-4x^3+4x-x^5+x^2-2\)
\(P\left(x\right)=\left(2x^3-4x^3\right)+\left(-3x+4x\right)+\left(x^5-x^5\right)+x^2-2\)
\(P\left(x\right)=-2x^3+x+x^2-2\)
Sắp xếp đa thức P:
\(P\left(x\right)=-2x^3+x^2+x-2\)
Thu gọn đa thức Q:
\(Q\left(x\right)=x^3-2x^2+3x+1+2x^2\)
\(Q\left(x\right)=x^3+\left(-2x^2+2x^2\right)+3x+1\)
\(Q\left(x\right)=x^3+3x+1\)
Sắp xếp đa thức Q:
\(Q\left(x\right)=x^3+3x+1\)
b) \(P\left(x\right)+Q\left(x\right)=\left(-2x^3+x^2+x-2\right)+\left(x^3+3x+1\right)\)
\(=-2x^3+x^2+x-2+x^3+3x+1\)
\(=\left(-2x^3+x^3\right)+x^2+\left(x+3x\right)+\left(-2+1\right)\)
\(=-x^3+x^2+4x+\left(-1\right)\)
\(=-x^3+x^2+4x-1\)
\(P\left(x\right)-Q\left(x\right)=\left(-2x^3+x^2+x-2\right)-\left(x^3+3x+1\right)\)
\(=-2x^3+x^2+x-2-x^3-3x-1\)
\(=\left(-2x^3-x^3\right)+x^2+\left(x-3x\right)+\left(-2-1\right)\)
\(=-3x^3+x^2+\left(-2x\right)+\left(-3\right)\)
\(=-3x^3+x^2-2x-3\)
\(M\left(x\right)=\left(-2x^3+x^2+x-2\right)+\left(x^3+3x+1\right)\)
\(=-2x^3+x^2+x-2+x^3+3x+1\)
\(=\left(-2x^3+x^3\right)+x^2+\left(x+3x\right)+\left(-2+1\right)\)
\(=-x^3+x^2+4x+\left(-1\right)\)
\(=-x^3+x^2+4x-1\)
Bậc của đa thức \(M\left(x\right)\) là: 3
