Question

Bài 4: Phân tích các đa thức sau thành nhân tử:

a) x³ - 2x² + x b) x² – 2x – 15

c) 5x²y³ – 25x³y⁴ + 10x³y³ d) 12x²y – 18xy² – 30y²

e) 5(x-y) – y.( x – y) f) y .( x – z) + 7(z - x)

g) 27x²( y- 1) – 9x³ ( 1 – y) h) 36 – 12x + x²

i) 3x³y² – 6x²y³ + 9x²y²

Answer 1

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

b) \(x^2-2x-15=\left(x^2-2x+1\right)-16=\left(x-1\right)^2-4^2=\left(x-1-4\right)\left(x-1+4\right)=\left(x-5\right)\left(x+3\right)\)

c) \(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)

d) \(12x^2y-18xy^2-30y^2=6\left(2x^2y-3xy^2-5y^2\right)\)

e, ntc: x-y

f, đối dấu --> ntc

g, như ý f

h, \(36-12x+x^2=\left(6-x\right)^2=\left(x-6\right)^2\)

i, \(3x^3y^2-6x^2y^3+9x^2y^2=3x^2y^2\left(x-y+3\right)\)