Question

Phân tích các đa thức sau thành nhân tử

a) x^4 - 8x

b) x^2 - 5x + 10y - 4y^2

c) 9y^2 - 4x^2 + 4x - 1

Answer 1

a) \(x^4-8x\)

\(=x\left(x^3-8\right)\)

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

b) \(x^2-5x+10y-4y^2\)

\(=\left(x^2-4y^2\right)-\left(5x-10y\right)\)

\(=\left(x-2y\right)\left(x+2y\right)-5\left(x-2y\right)\)

\(=\left(x-2y\right)\left(x+2y-5\right)\)

c) \(9y^2-4x^2+4x-1\)

\(=9y^2-\left(4x^2-4x+1\right)\)

\(=\left(3y\right)^2-\left(2x-1\right)^2\)

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

Answer 2

a) x⁴ - 8x

=x(x³-8)

=x(x-2)(x²+2x+4)

b) x² - 5x + 10y - 4y²

=(x²-4y²)-(5x-10y)

=(x-2y)(x+2y)-5(x-2y)

=(x-2y)(x+2y-5)

c) 9y² - 4x² + 4x - 1

=9y²-(4x²-4x+1)

=9y²-(2x+1)²

=[3y-(2x+1)][3y+(2x+1)]

=(3y-2x-1)(3y+2x+1)