Question

Phân tích đa thức thành nhân tử:
\(x^4+x^2-6\)

Answer 1

x^4+x^2−6

=(x^2)^2−x^2−6

đặt x^2=a

a^2-a-6

=(a−3)(a+2)

=(x^2−3)(x^2+2)

Answer 2

x⁴+x ²-6=x ⁴-2x²+ 3x²-6=x²(x²-2)+3(x²-2)=(x²-2)( x²-3)

Answer 3

\(x^4+x^2-6\)

\(=\left(x^2\right)^2+2x^2.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}-6\)

\(=\left(x^2+\dfrac{1}{2}\right)^2-\dfrac{25}{4}\)

\(=\left(x^2+\dfrac{1}{2}\right)^2-\left(\dfrac{5}{2}\right)^2\)

\(=\left(x^2+\dfrac{1}{2}-\dfrac{5}{2}\right)\left(x^2+\dfrac{1}{2}+\dfrac{5}{2}\right)\)

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