x^4 - 4x^3 - 8x^2 - 16x + 16
= x^4-8x^2+16-4x^3-16x
= ( x^2+4)^2 - 4x(x^2+4 )
= ( x^2 + 4 )(x^2 + 4 - 4x)
= (x^2 + 4 )( x - 2 )^2
\(x^4-4x^3+8x^2-16x+16\)
=\(x^4-4x^3+4x^2-16x+16\)
=\(x^2\left(x-2\right)^2+4\left(x-2\right)^2\)
=\(\left(x-2\right)^2\left(x^2+4\right)\)
x4 - 4x3 + 8x2 - 16x + 16 = x4 - 4x3 + 4x2+4x2 - 16x + 16= ( x4 - 4x3 + 4x2)+(4x2 - 16x + 16)
=x2(x2-4x+4) + 4( x2-4x+4) = (x2+4)(x2-4x+4)=(x2+4)(x-2)2
Phân tích đa thức thức thành nhân tử
x4 - 4x3 + 8x2 - 16x + 16
Giải:Ta có:\(x^4-4x^3+8x^2-16x+16\)
\(=x^4-2x^3-2x^3+4x^2+4x^2-8x-8x+16\)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x^3-2x^2+4x-8\right)\left(x-2\right)\)
\(=\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\left(x-2\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
