Use the discriminant to determine whether the quadratic polynomial can be factored?

Question

-8x^2-3x-5

Is the expression prime or can it be factored

Answer 1

If b^2 - 4ac has a nice whole number square root, then the polynomial can be factored.
Otherwise, the answer contains an irrational number and so it cannot be factored in terms of whole numbers or integers.
If a polynomial can be factored, that means it has rational numbers for zeros or roots. And you know rational numbers are just ratios of integers.
So to get to your example,
b^2 - 4ac = (-3)^2 - (4x(-8)x(-5) = 9 - -160 = 169
Since 169 has a nice whole number squre root (13^2 = 169). this polynomial can be factored.
However, it may be a bit difficult to factor, because you have a lead coefficient other than 0, and a composite number to boot. I have a trick for that, let me get you the link...
http://answers.yahoo.com/question/index;_ylt=AmRCG2H08L079xcc7uYIxpTsy6IX?qid=20070116093108AANHvgm