Question

Phân tích đa thức thành nhân tử:

x^4 - 4x^3 + 8x^2 - 16x + 16

Answer 1

\(x^4-4x^3+8x^2-16x+16\)

\(=\left(x^4+8x^2+16\right)-\left(4x^3+16x\right)\)

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

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

Answer 2

\(x^4-4x^3+8x^2-16x+16\)

\(\Rightarrow\left(\left(x^2\right)^2+8x^2+16\right)-\left(4x^3+16x\right)\)

\(\Rightarrow\left(x^2+4\right)^2-4x\left(x^2+4\right)\)

\(\Rightarrow\left(x^2+4\right)\left(x^2-4x+4\right)\)

\(\Rightarrow\left(x^2+4\right)\left(x-2\right)^2\)