Question

Phân tích đa thức thành nhân tử:

(\(^{x^2}\)+1)\(^2\)+3x(x\(^2\)+1)+2x\(^{^2}\)

Answer 1

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

\(=\left(x^2+1\right)^2+2\left(x^2+1\right)\dfrac{3}{2}x+\dfrac{9}{4}x^2-\dfrac{1}{4}x^2\)

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

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

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

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