Question

Phân tích đa thức thành nhân tử bằng cách thêm bớt :

a. x² - 5x + 4

b. 4x² - 4x - 3

Answer 1

a)\(x^2-5x+4\) 

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

\(=x\left(x-1\right)-4\left(x-1\right)\)

=\(\left(x-1\right)\left(x-4\right)\)

b)\(4x^2-4x-3\)

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

\(=2x\left(2x+1\right)-3\left(2x+1\right)\)

\(=\left(2x-3\right)\left(2x+1\right)\)

Answer 2

a) \(x^2-5x+4\)

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

\(=\left(x^2-4x+4\right)-x\)

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

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

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

b)  \(4x^2-4x-3\)

\(=4x^2-4x+1-4\)

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

\(=\left(2x+1-2\right)\left(2x+1+2\right)\)

\(=\left(2x-1\right)\left(2x+3\right)\)