Question

1. phân tích thành nhân tử : x³ - 12x + 1 - 12x²

Answer 1

\(x^3-12x^2-12x+1=x^3+x^2-13x^2-13x+x+1=x^2\left(x+1\right)-13x\left(x+1\right)+x+1=\left(x+1\right)\left(x^2-13x+1\right)\)

Answer 2

\(=\left(x^3+1\right)-12x\left(x+1\right)\)

= \(\left(x+1\right)\left(x^2-x+1\right)-12x\left(x+1\right)\)

= \(\left(x+1\right)\left(x^2-13x+1\right)\)

= \(\left(x+1\right)\left(x-\frac{13+\sqrt{165}}{2}\right)\left(x-\frac{13-\sqrt{165}}{2}\right)\)