Question

Phân tích đa thức thành nhân tử :

a) \(x^3-3x+2\) b) \(x^3+8x^2+17x+10\) c) \(x^3-2x-4\)

d) \(x^3+x^2+4\) e) \(x^3+9x^2+26x+24\) f) \(3x^3-14x^2+4x+3\)

Answer 1

a) \(x^3-3x+2=\left(x^3+8\right)-\left(3x+6\right)\)

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

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

b)\(x^3+8x^2+17x+10=\left(x^3+3x^2+2x\right)+\left(5x^2+15x+10\right)\)

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

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

c) \(x^3-2x-4=\left(x^3-8\right)-\left(2x-4\right)\)

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

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

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

e) Kết quả là: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\) bạn tự tách đi, đánh nhiều mỏi tay quá!:((

f) Kết quả là: \(\left(3x+1\right)\left(x^2-5x+3\right)\)