Question

   Phân tích đa thức thành nhân tử:

x⁴ + 7x³ + 14x² + 14x + 4

Answer 1

=x(x^3+7x^2+14x+14+4)

=x(x^3+7x^2+14x+18)

Answer 2

   x⁴+7x³+14x²+14x+4

=x⁴+7x³+4x²+10x²+14x+4

=(x⁴+4x²+4)+(7x³+14x)+10x²

=(x²+2)²+7x(x²+2)+10x²

=(x²+2)²+2x(x²+2)+5x(x²+2)+10x²

=(x²+2)(x²+2+2x)+5x(x²+2+2x)

=(x²+2+2x)(x²+2+5x)

Answer 3

\(x^4+7x^3+14x^2+14x+4\)

\(=x^4+x^3+6x^3+6x^2+8x^2+8x+4x+4\)

\(=x^3\left(x+1\right)+6x^2\left(x+1\right)+8x\left(x+1\right)+4\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3+6x^2+8x+4\right)\)