i want to noe what is the DIFERENCE between partial and complete factoring.

an e.g of a partial factoring problem is y=2x^2+8x+5

an e.g of complete factoring is y=x^2+3x-10

Form is ax^2 + bx + c

I can not factor the first example with whole numbers at all. b^2-4ac = 44 which is the square of no whole number.
The second one is
(x-2)(x+5)
note that b^2-4ac = 49 which is 7^2