Question

Разложить на множители многочлен:
1)2х²+х-3х³
2)у³-2у²+у
3)3ху²-х²у+х²у²
4)m³n²+2m²n³-m²n²
5)10а в4-ой b+15a³b²-5ab³
6)6c³d-12c²d³+18c³d²

Answer 1

1)2x²+x-3x³= -x(-2x-1+3x²) = -x(3x²-3x+x-1) = -x(3x(x-1) +(x-1))=- x(3x+1)(x-1)

2)y³-2y²+y = y (y²-2y +1) = y(y-1)² = y(y-1)(y-1)

3)3xy²-x²y +x²y² = xy(3y -x +xy)

4) m³n²+2m²n³ -m²n²= m²n² (m +2n -1)

5) 10a⁴b +15a³b²-5ab³ = 5ab (2a³+3a²b -b²)

6)6c³d -12c²d³+18c³d²= 6c²d (c -2d²+3cd)