Question

1. Phân tích các đa thức sau thành nhân tử

\(a.x^4+2x^3-4x-4\)

\(b.a^2b+b^2c+c^2a+ab^2+bc^2+ca^2+3abc\)

2. Tìm x biết

\(a.3x^4-10x^2-8=0\)

\(b.x^3+9x^2+26x+24=0\)

3. a.C/m\(\left(x^{3m+2}+x^{3n+1}\right)⋮\left(x^2+x+1\right)\)

(\(m,n\in N\))

b.Xác định a,b để

\(\left(ax^3+bx-24\right)⋮\left(x^2+4x+3\right)\)

Answer 1

Bài 1:

a, \(x^4+2x^3-4x-4\)

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

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

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

b, \(a^2b+b^2c+c^2a+ab^2+bc^2+ca^2+3abc\)

\(=\left(a^2b+a^2c+abc\right)+\left(b^2c+ab^2+abc\right)+\left(c^2a+bc^2+abc\right)\)

\(=a\left(ab+ac+bc\right)+b\left(bc+ab+bc\right)+c\left(ac+bc+ca\right)\)

\(=\left(a+b+c\right)\left(ab+ac+bc\right)\)