Question

Phân tích đa thức thành nhân tử

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

b, \(^{4x^4-21x^2y^2+y^4}\)

c, \(^{2\left(x^2+x\right)^2-\dfrac{1}{2}x^2}\)

Answer 1

b: \(=4x^4+4x^2y^2+y^4-25x^2y^2\)

\(=\left(2x^2+y^2\right)^2-25x^2y^2\)

\(=\left(2x^2-5xy+y^2\right)\left(2x^2+5xy+y^2\right)\)

c: \(=2\cdot x^2\cdot\left(x+1\right)^2-\dfrac{1}{2}x^2\)

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

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

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

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

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