Question

Phân tích đa thức thành nhân tử:

a,\(h\left(x\right)=x^4+3x^3+3x^2+3x+2\)

b,\(B=ab\left(a-b\right)\left(c+1\right)+bc\left(b-c\right)\left(a+1\right)+c\left(a-c\right)\left(b+1\right)\)

Answer 1

\(h\left(x\right)=x^4+3x^3+3x^2+3x+2\\ \Leftrightarrow h\left(x\right)=x^4+2x^3+x ^3+2x^2+x^2+2x+x+2\\ \Leftrightarrow h\left(x\right)=\left(x^4+2x^3\right)+\left(x^3+2x^2\right)+\left(x^2+2x\right)+\left(x+2\right)\\ \Leftrightarrow h\left(x\right)=x^3\left(x+2\right)+x^2\left(x+2\right)+x\left(x+2\right)+\left(x+2\right)\\ \Leftrightarrow h\left(x\right)=\left(x+2\right)\left(x^3+x^2+x+1\right)\\ \Leftrightarrow h\left(x\right)=\left(x+2\right)\left[x^2\left(x+1\right)+\left(x+1\right)\right]\\ \Leftrightarrow h\left(x\right)=\left(x+2\right)\left(x+1\right)\left(x^2+1\right)\)