Question

Dùng sơ đồ horner để ptdttnt

1, f(x)=\(x^3-7x-6\)

2, f(x)=\(x^3+4x^2-7x-10\)

Ai giúp mình với sáng mai nộp rồi

Answer 1

1. \(f\left(x\right)=x^3-7x-6\)

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

\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x+6\right)\)

\(=\left(x+1\right)\left(x^2+2x-3x-6\right)\)

\(=\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]\)

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

2/ \(f\left(x\right)=x^3+4x^2-7x-10\)

\(=x^3+5x^2-x^2-5x-2x-10\)

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

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

\(=\left(x+5\right)\left[\left(x^2-2x+x-2\right)\right]\)

\(=\left(x+5\right)\left[x\left(x-2\right)+\left(x-2\right)\right]\)

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