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15x^4 - 35x^3 + 10x^2
==> 5x^2 (3x^2 - 7x + 2) [Removing the common factor 5x^2]
==> 5x^2[3x^2 - 6x - x + 2] [Splitting the middle term]
==> 5x^2[3x(x-2) - 1(x-2)] [taking the common factor]
==>5x^2[(x-2)(3x-1)]
The factored form of the given expression = 5x^2[(x-2)(3x-1)]