Question

1.phân tích đa thức thành nhân tử:

x^4-3x^2+9

Answer 1

\(x^4-3x^2+9\)

\(=x^4+6x^2+9-9x^2\)

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

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

Answer 2

x⁴ - 3x² + 9 = x⁴ - 2.x².\(\frac{3}{2}\) + \(\frac{9}{4}\) + \(\frac{27}{4}\) = ( x² - \(\frac{3}{2}\) ) - \(\frac{27}{4}\) = ......ko biết .....

Answer 3

x⁴ -3x² +9  = x⁴ + 6x² +9 - 9x²

= (x² + 3)² - (3x)²

= (x² +3 - 3x)(x² +3+3x²)

Answer 4

\(x^4-\frac{3.2.x^2}{2}+\frac{9}{4}-\frac{27}{4}\)

\(=\left(x^2-\frac{3}{2}\right)^2-\sqrt{\frac{27}{4}}^2\)

\(=\left(x^2-\frac{3}{2}-\sqrt{\frac{27}{4}}\right)\left(x^2-\frac{3}{2}+\sqrt{\frac{27}{4}}\right)\)

oke :)

Answer 5

x^4 -3x^2 +9 = (x^4+6x^2 +9)-9x^2

                       = (x^2+3) -(3x)^2

                       = (x^2-3x+3)(x^2+3x+3)

Chúc bạn học tốt.