Разложить на множители многочлен:

1) 2 х²+х-3 х³

2) у³-2 у²+у

3) 3 ху²-х²у+х²у²

4) m³n²+2m²n³-m²n²

5) 10 а в4-ой b+15a³b²-5ab³

6) 6c³d-12c²d³+18c³d²

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)