Question

Phân tích đa thức thành nhân tử

A) x^3 + 4x - 5

B) x^3 - 6x^2 + 9x

C) x^2 - y^2 - x + y

Answer 1

a, = x³ - x² + x² - x + 5x - 5

= x².(x-1) +x.(x-1)+5.(x-1)

= (x-1).(x² + x +5)

b,=x.(x² - 6x +9)

= x.(x² -2.3.x +3²)=x.(x-3)²

^{c, = (x^2 -y^2 ) -(x-y) = (x-y).(x+y)-(x-y)=(x-y).(x+y-1)}

Answer 2

a)

\(x^3+4x-5\\ =x^3-x+5x-5\\ =\left(x-1\right)x\left(x+1\right)+5\left(x-1\right)\\ =\left(x-5\right)\left(x^2+x+5\right)\)

b)

\(x^3-6x^2+9x\\ =x^3-3x^2-3x^2+9x\\ =x^2\left(x-3\right)-3x\left(x-3\right)\\ =\left(x-3\right)\left(x^2-3x\right)\\ =\left(x-3\right)^2.x\)

c)

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