Question

Answer 1

Bài 1.

a) \(P\left(x\right)=-2x^4+4x^3-2x^4-2x^3-x^2+5\)

\(=\left(4x^3-2x^3\right)-\left(2x^4+2x^4\right)-x^2+5\)

\(=-4x^4+2x^3-x^2+5\)

\(Q\left(x\right)=2x^4-x^3-2x^2-1+x+x^3-x^2\)

\(=2x^4-\left(x^3-x^3\right)-\left(2x^2+x^2\right)+x+1\)

\(=2x^4-3x^2+x+1\)

b) \(P\left(x\right)-Q\left(x\right)=-4x^4+2x^3-x^2+5-\left(2x^4-3x^2+x+1\right)\)

\(=-4x^4+2x^3-x^2+5-2x^4+3x^2-x-1\)

\(=-\left(4x^4+2x^4\right)+2x^3+\left(3x^2-x^2\right)-x+\left(5-1\right)\)

\(=-6x^4+2x^3+2x^2-x+4\)

\(P\left(-1\right)=2.\left(-1\right)^3-4.\left(-1\right)^4-\left(-1\right)^2+5\)

\(=5-4-2-1=-2\)

\(Q\left(2\right)=2.2^4-3.2^2+2+1\)

\(=32-12+2+1=23\)