Question

Phân tích đa thức thành nhân tử:

a, \(x^4+6x^3+7x^2-6x+1\)

b, \(x^4-7x^3+14x^2-7x+1\)

c, \(12x^2-11x-36\)

Answer 1

a, \(x^4+6x^3+7x^2-6x+1\)

\(=x^4-2x^2+1+6x^3+9x^2+6x\)

\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)

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

b, \(x^4-7x^3+14x^2-7x+1\)

\(=x^4+2x^2+1+7x^3+12x^2-7x\)

\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)

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

c, \(12x^2-11x-36\)

\(=12x^2-27x+16x-36\)

\(=3x\left(4x-9\right)+4\left(4x-9\right)\)

\(=\left(4x-9\right)\left(3x+4\right)\)