Question

1) Phân tích các đa thức sau thành nhân tử
a) x^3 - 6x^2 + 11x - 6
b) x^3 - 6x^2 - 9x+ 14
c) x^3+ 6x^2+ 11x+ 6
d)x^5+ x^4+ x^3+ x^2+ x+ 1
e) x^6 - 9x^3 + 8
g) x^6 + 27
2) Tìm x , biết
a) (x+3)^4 - (x-3)^4 - 24x^3 = 108
b) (x+2)^5 - (x-2)^5 = 64

Answer 1

Bài 1: 

a: \(x^3-6x^2+11x-6\)

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

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

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

b: \(x^3-6x^2-9x+14\)

\(=x^3-7x^2+x^2-7x-2x+14\)

\(=\left(x-7\right)\left(x^2+x-2\right)\)

\(=\left(x-7\right)\left(x+2\right)\left(x-1\right)\)

c: \(x^3+6x^2+11x+6\)

\(=x^3+3x^2+3x^2+9x+2x+6\)

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

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