Given 4x2+4x-1
Using the formula for the roots of quadratic equation, (-b +/-./b2-4ac)/2a
the roots for the above will be (-4+/-4./2)/8 = (-1+/-./2)/2
Hence the two roots are (-1+./2)/2 and (-1-./2)/2
As the roots are irrational, there is no possibility of getting factors.
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(2x-1)(2x-1) = 4x^2 -4x + 1
16x2 + 8x + 1 - 9y2 = (4x + 1)2 - (3y)2 which is a difference of two squares. = (4x + 1 + 3y)*(4x + 1 - 3y)
(x + 1)(2x + 5)
3(x2 + 3x + 1)
(x2 - x + 1)(x2 + x + 1)