Question

Phân tích đa thức thành nhân tử: \(x^2-\sqrt{x}+x-1\)

Answer 1

\(x^2-\sqrt{x}+x-1\)

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

=\(\left(x+1\right)\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)+\sqrt{x}\left(\sqrt{x}-1\right)\)

=\(\left(\sqrt{x}-1\right)\left(x\sqrt{x}+x+\sqrt{x}+1+\sqrt{x}\right)\)

=\(\left(\sqrt{x}-1\right)\left(x\sqrt{x}+x+2\sqrt{x}+1\right)\)

Answer 2

\(x^2-\sqrt{x}+x-1\)

\(=\sqrt{x}\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)

\(=\left(\sqrt{x}-1\right)\left(\sqrt{x}+\sqrt{x}+1\right)\)

\(=\left(\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)\)