Question

Phân tích đa thức thành nhân tử:

a) x²+3xy-2y²

b) x⁴+x²+2x

c) x⁴-3x²+1

d)4x.(x-2y)+16y²-8xy

e)3x.(x+1)²-5x².(x+1)+7x+7

f) 2ax²-3bx²+2ay-3by+4a-6b

Answer 1

b: \(=x\left(x^3+x^2+2\right)\)

c: \(=x^4-2x^2+1-x^2\)

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

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

d: \(=4x\left(x-2y\right)+8y\left(2y-x\right)\)

\(=\left(x-2y\right)\left(4x-8y\right)\)

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

e: \(=3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)

\(=\left(x+1\right)\left[3x\left(x+1\right)-5x^2+7\right]\)

\(=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)\)

\(=\left(x+1\right)\left(-2x^2+3x+7\right)\)