Question

phân tích đa thức sau thành nhân tử:

a) x^3-6x^2+11x-6

b) x^3-19x-30

Answer 1

a,

\(x^3-6x^2+11x-6=x^3-x^2-5x^2+5x+6x-6\)

\(=x^2\left(x-1\right)-5x\left(x-1\right)+6\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-5x+6\right)\)

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

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

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

b,

\(x^3-19x-30=x^3-5x^2+5x^2-25x+6x-30\)

\(=x^2\left(x-5\right)+5x\left(x-5\right)-6\left(x-5\right)\)

\(=\left(x-5\right)\left(x^2+5x-6\right)\)

\(=\left(x-5\right)\left(x^2-6x+x-6\right)\)

\(=\left(x-5\right)\left[x\left(x-6\right)+\left(x-6\right)\right]\)

\(=\left(x-5\right)\left(x+1\right)\left(x-6\right)\)