Question

Phân tích đa thức sau thành nhân tử

a) 7x² - 8x + 1

b) (x² + 2x)² + 9x² + 18x + 20

c) (2x - 1)² + (2x - 1)y - 2y²

d) x⁴ - 13x² + 36

Answer 1

a/ \(=7x^2-7x-x+1=7x\left(x-1\right)-\left(x-1\right)=\left(7x-1\right)\left(x-1\right)\)

b/ \(=\left(x^2+2x\right)^2+4\left(x^2+2x\right)+5\left(x^2+2x\right)+20\)

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

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

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

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

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

d/ \(=x^4-9x^2-4x^2+36=x^2\left(x^2-9\right)-4\left(x^2-9\right)\)

\(=\left(x^2-4\right)\left(x^2-9\right)=\left(x-2\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)