12(x^2) + 16x - 3
*** notice no equal signs, the following is not equivalent to each other
move coefficient
x^2 + 16x - 36 (3 * 12)
factor that
(X + 18) (X - 2)
re-put the 12
X+ 18/12 X - 2/12
simplify
X + 3/2 x - 1/6
move denominator
All that was just a math pattern, this is the actual factor:
(2x+3)(6x-1)
its kind of weird looking I know but if you re-multiply out you get:
12x^2 + 18x - 2x -3
VOILA!
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x2 + 12x2 + 35 = 13x2 + 35 which cannot be factorised in any sensible way.
Factor out an X X(X^2 - 12X + 35) factor quadratic equation X(X - 7)(X - 5) ------------------- fully factored
12x2-23x+10 = (3x-2)(4x-5) when factored
4x(4x^2 - 6x + 7)
The GCF is 6x.