Question

Phân tích thành nhân tử:

a. x² - 3;                                                    b. x² - 6;

c. \(x^2+2\sqrt{3}x+3;\)                                   d. \(x^2-2\sqrt{5}x+5.\)

 

Answer 1

a) x²-3=(x-\(\sqrt{3}\))(x+\(\sqrt{3}\))

b) x²-6=(x-\(\sqrt{6}\))(x+\(\sqrt{6}\))

c) x²+2\(\sqrt{3}\)x +3 = x² + 2.x.\(\sqrt{3}\) + (\(\sqrt{3}\))²= (x+\(\sqrt{3}\))²=(x+\(\sqrt{3}\))(x+\(\sqrt{3}\)).

d) x²-2\(\sqrt{5}\) x+ 5 = x² - 2.x.\(\sqrt{5}\) + (\(\sqrt{5}\))² = (x-\(\sqrt{5}\))²= (x-\(\sqrt{5}\))(x-\(\sqrt{5}\)).

Answer 2

a) \(x^2-3=x^2-\left(\sqrt{3}\right)^2=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)

b) \(x^2-6=x^2-\left(\sqrt{6}\right)^2=\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)

c) \(x^2+2\sqrt{3}x+3=x^2+2.x.\sqrt{3}+\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)^2\)

d) \(x^2-2\sqrt{5}x+5=x^2-2.x.\sqrt{5}+\left(\sqrt{5}\right)^2=\left(x-\sqrt{5}\right)^2\)